model_theory.substructures | 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

0602c598

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

6cf59007

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -256,7 +256,7 @@ theorem mem_sInf {S : Set (L.Substructure M)} {x : M} : x ∈ sInf S ↔ ∀ p 
 
 #print FirstOrder.Language.Substructure.mem_iInf /-
 theorem mem_iInf {ι : Sort _} {S : ι → L.Substructure M} {x : M} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i :=
-  by simp only [iInf, mem_Inf, Set.forall_range_iff]
+  by simp only [iInf, mem_Inf, Set.forall_mem_range]
 #align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_iInf
 -/
 
@@ -911,10 +911,10 @@ def substructureReduct : L'.Substructure M ↪o L.Substructure M
       fun_mem := fun n f x hx =>
         by
         have h := S.fun_mem (φ.on_function f) x hx
-        simp only [Lhom.map_on_function, substructure.mem_carrier] at h 
+        simp only [Lhom.map_on_function, substructure.mem_carrier] at h
         exact h }
   inj' S T h := by
-    simp only [SetLike.coe_set_eq] at h 
+    simp only [SetLike.coe_set_eq] at h
     exact h
   map_rel_iff' S T := Iff.rfl
 #align first_order.language.Lhom.substructure_reduct FirstOrder.Language.LHom.substructureReduct

6cf59007

bump to nightly-2024-02-07-08

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

8a1bf67e

Diff

@@ -1022,7 +1022,7 @@ hom `M → p`. -/
 def codRestrict (p : L.Substructure N) (f : M →[L] N) (h : ∀ c, f c ∈ p) : M →[L] p
     where
   toFun c := ⟨f c, h c⟩
-  map_rel' n R x h := f.map_rel R x h
+  map_rel' n R x h := f.mapRel R x h
 #align first_order.language.hom.cod_restrict FirstOrder.Language.Hom.codRestrict
 -/

6cf59007

bump to nightly-2023-12-22-06

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

485b2c6c

Diff

@@ -328,7 +328,7 @@ open Set
 /-- A substructure `S` includes `closure L s` if and only if it includes `s`. -/
 @[simp]
 theorem closure_le : closure L s ≤ S ↔ s ⊆ S :=
-  (closure L).closure_le_closed_iff_le s S.closed
+  (closure L).closure_le_iff s S.closed
 #align first_order.language.substructure.closure_le FirstOrder.Language.Substructure.closure_le
 -/

6cf59007

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2021 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 -/
-import Mathbin.Order.Closure
-import Mathbin.ModelTheory.Semantics
-import Mathbin.ModelTheory.Encoding
+import Order.Closure
+import ModelTheory.Semantics
+import ModelTheory.Encoding
 
 #align_import model_theory.substructures from "leanprover-community/mathlib"@"6cf5900728239efa287df7761ec2a1ac9cf39b29"

6cf59007

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module model_theory.substructures
-! leanprover-community/mathlib commit 6cf5900728239efa287df7761ec2a1ac9cf39b29
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Order.Closure
 import Mathbin.ModelTheory.Semantics
 import Mathbin.ModelTheory.Encoding
 
+#align_import model_theory.substructures from "leanprover-community/mathlib"@"6cf5900728239efa287df7761ec2a1ac9cf39b29"
+
 /-!
 # First-Order Substructures

6cf59007

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -82,13 +82,17 @@ variable {L f s} {t : Set M}
 
 namespace ClosedUnder
 
+#print FirstOrder.Language.ClosedUnder.inter /-
 theorem inter (hs : ClosedUnder f s) (ht : ClosedUnder f t) : ClosedUnder f (s ∩ t) := fun x h =>
   mem_inter (hs x fun i => mem_of_mem_inter_left (h i)) (ht x fun i => mem_of_mem_inter_right (h i))
 #align first_order.language.closed_under.inter FirstOrder.Language.ClosedUnder.inter
+-/
 
+#print FirstOrder.Language.ClosedUnder.inf /-
 theorem inf (hs : ClosedUnder f s) (ht : ClosedUnder f t) : ClosedUnder f (s ⊓ t) :=
   hs.inter ht
 #align first_order.language.closed_under.inf FirstOrder.Language.ClosedUnder.inf
+-/
 
 variable {S : Set (Set M)}
 
@@ -156,12 +160,14 @@ end Substructure
 
 variable {S : L.Substructure M}
 
+#print FirstOrder.Language.Term.realize_mem /-
 theorem Term.realize_mem {α : Type _} (t : L.term α) (xs : α → M) (h : ∀ a, xs a ∈ S) :
     t.realize xs ∈ S := by
   induction' t with a n f ts ih
   · exact h a
   · exact substructure.fun_mem _ _ _ ih
 #align first_order.language.term.realize_mem FirstOrder.Language.Term.realize_mem
+-/
 
 namespace Substructure
 
@@ -178,9 +184,11 @@ theorem copy_eq {s : Set M} (hs : s = S) : S.copy s hs = S :=
 #align first_order.language.substructure.copy_eq FirstOrder.Language.Substructure.copy_eq
 -/
 
+#print FirstOrder.Language.Substructure.constants_mem /-
 theorem constants_mem (c : L.Constants) : ↑c ∈ S :=
   mem_carrier.2 (S.fun_mem c _ Fin.elim0)
 #align first_order.language.substructure.constants_mem FirstOrder.Language.Substructure.constants_mem
+-/
 
 /-- The substructure `M` of the structure `M`. -/
 instance : Top (L.Substructure M) :=
@@ -210,10 +218,12 @@ instance : Inf (L.Substructure M) :=
     { carrier := S₁ ∩ S₂
       fun_mem := fun n f => (S₁.fun_mem f).inf (S₂.fun_mem f) }⟩
 
+#print FirstOrder.Language.Substructure.coe_inf /-
 @[simp]
 theorem coe_inf (p p' : L.Substructure M) : ((p ⊓ p' : L.Substructure M) : Set M) = p ∩ p' :=
   rfl
 #align first_order.language.substructure.coe_inf FirstOrder.Language.Substructure.coe_inf
+-/
 
 #print FirstOrder.Language.Substructure.mem_inf /-
 @[simp]
@@ -247,14 +257,18 @@ theorem mem_sInf {S : Set (L.Substructure M)} {x : M} : x ∈ sInf S ↔ ∀ p 
 #align first_order.language.substructure.mem_Inf FirstOrder.Language.Substructure.mem_sInf
 -/
 
+#print FirstOrder.Language.Substructure.mem_iInf /-
 theorem mem_iInf {ι : Sort _} {S : ι → L.Substructure M} {x : M} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i :=
   by simp only [iInf, mem_Inf, Set.forall_range_iff]
 #align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_iInf
+-/
 
+#print FirstOrder.Language.Substructure.coe_iInf /-
 @[simp, norm_cast]
 theorem coe_iInf {ι : Sort _} {S : ι → L.Substructure M} : (↑(⨅ i, S i) : Set M) = ⋂ i, S i := by
   simp only [iInf, coe_Inf, Set.biInter_range]
 #align first_order.language.substructure.coe_infi FirstOrder.Language.Substructure.coe_iInf
+-/
 
 /-- Substructures of a structure form a complete lattice. -/
 instance : CompleteLattice (L.Substructure M) :=
@@ -274,11 +288,13 @@ instance : CompleteLattice (L.Substructure M) :=
 
 variable (L)
 
+#print FirstOrder.Language.Substructure.closure /-
 /-- The `L.substructure` generated by a set. -/
 def closure : LowerAdjoint (coe : L.Substructure M → Set M) :=
   ⟨fun s => sInf {S | s ⊆ S}, fun s S =>
     ⟨Set.Subset.trans fun x hx => mem_sInf.2 fun S hS => hS hx, fun h => sInf_le h⟩⟩
 #align first_order.language.substructure.closure FirstOrder.Language.Substructure.closure
+-/
 
 variable {L} {s : Set M}
 
@@ -311,21 +327,27 @@ theorem closed (S : L.Substructure M) : (closure L).closed (S : Set M) :=
 
 open Set
 
+#print FirstOrder.Language.Substructure.closure_le /-
 /-- A substructure `S` includes `closure L s` if and only if it includes `s`. -/
 @[simp]
 theorem closure_le : closure L s ≤ S ↔ s ⊆ S :=
   (closure L).closure_le_closed_iff_le s S.closed
 #align first_order.language.substructure.closure_le FirstOrder.Language.Substructure.closure_le
+-/
 
+#print FirstOrder.Language.Substructure.closure_mono /-
 /-- Substructure closure of a set is monotone in its argument: if `s ⊆ t`,
 then `closure L s ≤ closure L t`. -/
 theorem closure_mono ⦃s t : Set M⦄ (h : s ⊆ t) : closure L s ≤ closure L t :=
   (closure L).Monotone h
 #align first_order.language.substructure.closure_mono FirstOrder.Language.Substructure.closure_mono
+-/
 
+#print FirstOrder.Language.Substructure.closure_eq_of_le /-
 theorem closure_eq_of_le (h₁ : s ⊆ S) (h₂ : S ≤ closure L s) : closure L s = S :=
   (closure L).eq_of_le h₁ h₂
 #align first_order.language.substructure.closure_eq_of_le FirstOrder.Language.Substructure.closure_eq_of_le
+-/
 
 #print FirstOrder.Language.Substructure.coe_closure_eq_range_term_realize /-
 theorem coe_closure_eq_range_term_realize :
@@ -367,6 +389,7 @@ theorem lift_card_closure_le_card_term : Cardinal.lift.{max u w} (#closure L s)
 #align first_order.language.substructure.lift_card_closure_le_card_term FirstOrder.Language.Substructure.lift_card_closure_le_card_term
 -/
 
+#print FirstOrder.Language.Substructure.lift_card_closure_le /-
 theorem lift_card_closure_le :
     Cardinal.lift.{u, w} (#closure L s) ≤
       max ℵ₀ (Cardinal.lift.{u, w} (#s) + Cardinal.lift.{w, u} (#Σ i, L.Functions i)) :=
@@ -375,6 +398,7 @@ theorem lift_card_closure_le :
   refine' lift_card_closure_le_card_term.trans (term.card_le.trans _)
   rw [mk_sum, lift_umax]
 #align first_order.language.substructure.lift_card_closure_le FirstOrder.Language.Substructure.lift_card_closure_le
+-/
 
 variable (L)
 
@@ -415,6 +439,7 @@ theorem dense_induction {p : M → Prop} (x : M) {s : Set M} (hs : closure L s =
 
 variable (L) (M)
 
+#print FirstOrder.Language.Substructure.gi /-
 /-- `closure` forms a Galois insertion with the coercion to set. -/
 protected def gi : GaloisInsertion (@closure L M _) coe
     where
@@ -423,6 +448,7 @@ protected def gi : GaloisInsertion (@closure L M _) coe
   le_l_u s := subset_closure
   choice_eq s h := rfl
 #align first_order.language.substructure.gi FirstOrder.Language.Substructure.gi
+-/
 
 variable {L} {M}
 
@@ -434,10 +460,12 @@ theorem closure_eq : closure L (S : Set M) = S :=
 #align first_order.language.substructure.closure_eq FirstOrder.Language.Substructure.closure_eq
 -/
 
+#print FirstOrder.Language.Substructure.closure_empty /-
 @[simp]
 theorem closure_empty : closure L (∅ : Set M) = ⊥ :=
   (Substructure.gi L M).gc.l_bot
 #align first_order.language.substructure.closure_empty FirstOrder.Language.Substructure.closure_empty
+-/
 
 #print FirstOrder.Language.Substructure.closure_univ /-
 @[simp]
@@ -446,19 +474,25 @@ theorem closure_univ : closure L (univ : Set M) = ⊤ :=
 #align first_order.language.substructure.closure_univ FirstOrder.Language.Substructure.closure_univ
 -/
 
+#print FirstOrder.Language.Substructure.closure_union /-
 theorem closure_union (s t : Set M) : closure L (s ∪ t) = closure L s ⊔ closure L t :=
   (Substructure.gi L M).gc.l_sup
 #align first_order.language.substructure.closure_union FirstOrder.Language.Substructure.closure_union
+-/
 
+#print FirstOrder.Language.Substructure.closure_unionᵢ /-
 theorem closure_unionᵢ {ι} (s : ι → Set M) : closure L (⋃ i, s i) = ⨆ i, closure L (s i) :=
   (Substructure.gi L M).gc.l_iSup
 #align first_order.language.substructure.closure_Union FirstOrder.Language.Substructure.closure_unionᵢ
+-/
 
+#print FirstOrder.Language.Substructure.small_bot /-
 instance small_bot : Small.{u} (⊥ : L.Substructure M) :=
   by
   rw [← closure_empty]
   exact substructure.small_closure
 #align first_order.language.substructure.small_bot FirstOrder.Language.Substructure.small_bot
+-/
 
 /-!
 ### `comap` and `map`
@@ -477,20 +511,26 @@ def comap (φ : M →[L] N) (S : L.Substructure N) : L.Substructure M
 #align first_order.language.substructure.comap FirstOrder.Language.Substructure.comap
 -/
 
+#print FirstOrder.Language.Substructure.mem_comap /-
 @[simp]
 theorem mem_comap {S : L.Substructure N} {f : M →[L] N} {x : M} : x ∈ S.comap f ↔ f x ∈ S :=
   Iff.rfl
 #align first_order.language.substructure.mem_comap FirstOrder.Language.Substructure.mem_comap
+-/
 
+#print FirstOrder.Language.Substructure.comap_comap /-
 theorem comap_comap (S : L.Substructure P) (g : N →[L] P) (f : M →[L] N) :
     (S.comap g).comap f = S.comap (g.comp f) :=
   rfl
 #align first_order.language.substructure.comap_comap FirstOrder.Language.Substructure.comap_comap
+-/
 
+#print FirstOrder.Language.Substructure.comap_id /-
 @[simp]
 theorem comap_id (S : L.Substructure P) : S.comap (Hom.id _ _) = S :=
   ext (by simp)
 #align first_order.language.substructure.comap_id FirstOrder.Language.Substructure.comap_id
+-/
 
 #print FirstOrder.Language.Substructure.map /-
 /-- The image of a substructure along a homomorphism is a substructure. -/
@@ -508,95 +548,135 @@ def map (φ : M →[L] N) (S : L.Substructure M) : L.Substructure N
 #align first_order.language.substructure.map FirstOrder.Language.Substructure.map
 -/
 
+#print FirstOrder.Language.Substructure.mem_map /-
 @[simp]
 theorem mem_map {f : M →[L] N} {S : L.Substructure M} {y : N} : y ∈ S.map f ↔ ∃ x ∈ S, f x = y :=
   mem_image_iff_bex
 #align first_order.language.substructure.mem_map FirstOrder.Language.Substructure.mem_map
+-/
 
+#print FirstOrder.Language.Substructure.mem_map_of_mem /-
 theorem mem_map_of_mem (f : M →[L] N) {S : L.Substructure M} {x : M} (hx : x ∈ S) : f x ∈ S.map f :=
   mem_image_of_mem f hx
 #align first_order.language.substructure.mem_map_of_mem FirstOrder.Language.Substructure.mem_map_of_mem
+-/
 
+#print FirstOrder.Language.Substructure.apply_coe_mem_map /-
 theorem apply_coe_mem_map (f : M →[L] N) (S : L.Substructure M) (x : S) : f x ∈ S.map f :=
   mem_map_of_mem f x.Prop
 #align first_order.language.substructure.apply_coe_mem_map FirstOrder.Language.Substructure.apply_coe_mem_map
+-/
 
+#print FirstOrder.Language.Substructure.map_map /-
 theorem map_map (g : N →[L] P) (f : M →[L] N) : (S.map f).map g = S.map (g.comp f) :=
   SetLike.coe_injective <| image_image _ _ _
 #align first_order.language.substructure.map_map FirstOrder.Language.Substructure.map_map
+-/
 
+#print FirstOrder.Language.Substructure.map_le_iff_le_comap /-
 theorem map_le_iff_le_comap {f : M →[L] N} {S : L.Substructure M} {T : L.Substructure N} :
     S.map f ≤ T ↔ S ≤ T.comap f :=
   image_subset_iff
 #align first_order.language.substructure.map_le_iff_le_comap FirstOrder.Language.Substructure.map_le_iff_le_comap
+-/
 
+#print FirstOrder.Language.Substructure.gc_map_comap /-
 theorem gc_map_comap (f : M →[L] N) : GaloisConnection (map f) (comap f) := fun S T =>
   map_le_iff_le_comap
 #align first_order.language.substructure.gc_map_comap FirstOrder.Language.Substructure.gc_map_comap
+-/
 
+#print FirstOrder.Language.Substructure.map_le_of_le_comap /-
 theorem map_le_of_le_comap {T : L.Substructure N} {f : M →[L] N} : S ≤ T.comap f → S.map f ≤ T :=
   (gc_map_comap f).l_le
 #align first_order.language.substructure.map_le_of_le_comap FirstOrder.Language.Substructure.map_le_of_le_comap
+-/
 
+#print FirstOrder.Language.Substructure.le_comap_of_map_le /-
 theorem le_comap_of_map_le {T : L.Substructure N} {f : M →[L] N} : S.map f ≤ T → S ≤ T.comap f :=
   (gc_map_comap f).le_u
 #align first_order.language.substructure.le_comap_of_map_le FirstOrder.Language.Substructure.le_comap_of_map_le
+-/
 
+#print FirstOrder.Language.Substructure.le_comap_map /-
 theorem le_comap_map {f : M →[L] N} : S ≤ (S.map f).comap f :=
   (gc_map_comap f).le_u_l _
 #align first_order.language.substructure.le_comap_map FirstOrder.Language.Substructure.le_comap_map
+-/
 
+#print FirstOrder.Language.Substructure.map_comap_le /-
 theorem map_comap_le {S : L.Substructure N} {f : M →[L] N} : (S.comap f).map f ≤ S :=
   (gc_map_comap f).l_u_le _
 #align first_order.language.substructure.map_comap_le FirstOrder.Language.Substructure.map_comap_le
+-/
 
+#print FirstOrder.Language.Substructure.monotone_map /-
 theorem monotone_map {f : M →[L] N} : Monotone (map f) :=
   (gc_map_comap f).monotone_l
 #align first_order.language.substructure.monotone_map FirstOrder.Language.Substructure.monotone_map
+-/
 
+#print FirstOrder.Language.Substructure.monotone_comap /-
 theorem monotone_comap {f : M →[L] N} : Monotone (comap f) :=
   (gc_map_comap f).monotone_u
 #align first_order.language.substructure.monotone_comap FirstOrder.Language.Substructure.monotone_comap
+-/
 
+#print FirstOrder.Language.Substructure.map_comap_map /-
 @[simp]
 theorem map_comap_map {f : M →[L] N} : ((S.map f).comap f).map f = S.map f :=
   (gc_map_comap f).l_u_l_eq_l _
 #align first_order.language.substructure.map_comap_map FirstOrder.Language.Substructure.map_comap_map
+-/
 
+#print FirstOrder.Language.Substructure.comap_map_comap /-
 @[simp]
 theorem comap_map_comap {S : L.Substructure N} {f : M →[L] N} :
     ((S.comap f).map f).comap f = S.comap f :=
   (gc_map_comap f).u_l_u_eq_u _
 #align first_order.language.substructure.comap_map_comap FirstOrder.Language.Substructure.comap_map_comap
+-/
 
+#print FirstOrder.Language.Substructure.map_sup /-
 theorem map_sup (S T : L.Substructure M) (f : M →[L] N) : (S ⊔ T).map f = S.map f ⊔ T.map f :=
   (gc_map_comap f).l_sup
 #align first_order.language.substructure.map_sup FirstOrder.Language.Substructure.map_sup
+-/
 
+#print FirstOrder.Language.Substructure.map_iSup /-
 theorem map_iSup {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure M) :
     (iSup s).map f = ⨆ i, (s i).map f :=
   (gc_map_comap f).l_iSup
 #align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_iSup
+-/
 
+#print FirstOrder.Language.Substructure.comap_inf /-
 theorem comap_inf (S T : L.Substructure N) (f : M →[L] N) :
     (S ⊓ T).comap f = S.comap f ⊓ T.comap f :=
   (gc_map_comap f).u_inf
 #align first_order.language.substructure.comap_inf FirstOrder.Language.Substructure.comap_inf
+-/
 
+#print FirstOrder.Language.Substructure.comap_iInf /-
 theorem comap_iInf {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure N) :
     (iInf s).comap f = ⨅ i, (s i).comap f :=
   (gc_map_comap f).u_iInf
 #align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_iInf
+-/
 
+#print FirstOrder.Language.Substructure.map_bot /-
 @[simp]
 theorem map_bot (f : M →[L] N) : (⊥ : L.Substructure M).map f = ⊥ :=
   (gc_map_comap f).l_bot
 #align first_order.language.substructure.map_bot FirstOrder.Language.Substructure.map_bot
+-/
 
+#print FirstOrder.Language.Substructure.comap_top /-
 @[simp]
 theorem comap_top (f : M →[L] N) : (⊤ : L.Substructure N).comap f = ⊤ :=
   (gc_map_comap f).u_top
 #align first_order.language.substructure.comap_top FirstOrder.Language.Substructure.comap_top
+-/
 
 #print FirstOrder.Language.Substructure.map_id /-
 @[simp]
@@ -605,65 +685,87 @@ theorem map_id (S : L.Substructure M) : S.map (Hom.id L M) = S :=
 #align first_order.language.substructure.map_id FirstOrder.Language.Substructure.map_id
 -/
 
+#print FirstOrder.Language.Substructure.map_closure /-
 theorem map_closure (f : M →[L] N) (s : Set M) : (closure L s).map f = closure L (f '' s) :=
   Eq.symm <|
     closure_eq_of_le (Set.image_subset f subset_closure) <|
       map_le_iff_le_comap.2 <| closure_le.2 fun x hx => subset_closure ⟨x, hx, rfl⟩
 #align first_order.language.substructure.map_closure FirstOrder.Language.Substructure.map_closure
+-/
 
+#print FirstOrder.Language.Substructure.closure_image /-
 @[simp]
 theorem closure_image (f : M →[L] N) : closure L (f '' s) = map f (closure L s) :=
   (map_closure f s).symm
 #align first_order.language.substructure.closure_image FirstOrder.Language.Substructure.closure_image
+-/
 
 section GaloisCoinsertion
 
 variable {ι : Type _} {f : M →[L] N} (hf : Function.Injective f)
 
-include hf
-
+#print FirstOrder.Language.Substructure.gciMapComap /-
 /-- `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. -/
 def gciMapComap : GaloisCoinsertion (map f) (comap f) :=
   (gc_map_comap f).toGaloisCoinsertion fun S x => by simp [mem_comap, mem_map, hf.eq_iff]
 #align first_order.language.substructure.gci_map_comap FirstOrder.Language.Substructure.gciMapComap
+-/
 
+#print FirstOrder.Language.Substructure.comap_map_eq_of_injective /-
 theorem comap_map_eq_of_injective (S : L.Substructure M) : (S.map f).comap f = S :=
   (gciMapComap hf).u_l_eq _
 #align first_order.language.substructure.comap_map_eq_of_injective FirstOrder.Language.Substructure.comap_map_eq_of_injective
+-/
 
+#print FirstOrder.Language.Substructure.comap_surjective_of_injective /-
 theorem comap_surjective_of_injective : Function.Surjective (comap f) :=
   (gciMapComap hf).u_surjective
 #align first_order.language.substructure.comap_surjective_of_injective FirstOrder.Language.Substructure.comap_surjective_of_injective
+-/
 
+#print FirstOrder.Language.Substructure.map_injective_of_injective /-
 theorem map_injective_of_injective : Function.Injective (map f) :=
   (gciMapComap hf).l_injective
 #align first_order.language.substructure.map_injective_of_injective FirstOrder.Language.Substructure.map_injective_of_injective
+-/
 
+#print FirstOrder.Language.Substructure.comap_inf_map_of_injective /-
 theorem comap_inf_map_of_injective (S T : L.Substructure M) : (S.map f ⊓ T.map f).comap f = S ⊓ T :=
   (gciMapComap hf).u_inf_l _ _
 #align first_order.language.substructure.comap_inf_map_of_injective FirstOrder.Language.Substructure.comap_inf_map_of_injective
+-/
 
+#print FirstOrder.Language.Substructure.comap_iInf_map_of_injective /-
 theorem comap_iInf_map_of_injective (S : ι → L.Substructure M) :
     (⨅ i, (S i).map f).comap f = iInf S :=
   (gciMapComap hf).u_iInf_l _
 #align first_order.language.substructure.comap_infi_map_of_injective FirstOrder.Language.Substructure.comap_iInf_map_of_injective
+-/
 
+#print FirstOrder.Language.Substructure.comap_sup_map_of_injective /-
 theorem comap_sup_map_of_injective (S T : L.Substructure M) : (S.map f ⊔ T.map f).comap f = S ⊔ T :=
   (gciMapComap hf).u_sup_l _ _
 #align first_order.language.substructure.comap_sup_map_of_injective FirstOrder.Language.Substructure.comap_sup_map_of_injective
+-/
 
+#print FirstOrder.Language.Substructure.comap_iSup_map_of_injective /-
 theorem comap_iSup_map_of_injective (S : ι → L.Substructure M) :
     (⨆ i, (S i).map f).comap f = iSup S :=
   (gciMapComap hf).u_iSup_l _
 #align first_order.language.substructure.comap_supr_map_of_injective FirstOrder.Language.Substructure.comap_iSup_map_of_injective
+-/
 
+#print FirstOrder.Language.Substructure.map_le_map_iff_of_injective /-
 theorem map_le_map_iff_of_injective {S T : L.Substructure M} : S.map f ≤ T.map f ↔ S ≤ T :=
   (gciMapComap hf).l_le_l_iff
 #align first_order.language.substructure.map_le_map_iff_of_injective FirstOrder.Language.Substructure.map_le_map_iff_of_injective
+-/
 
+#print FirstOrder.Language.Substructure.map_strictMono_of_injective /-
 theorem map_strictMono_of_injective : StrictMono (map f) :=
   (gciMapComap hf).strictMono_l
 #align first_order.language.substructure.map_strict_mono_of_injective FirstOrder.Language.Substructure.map_strictMono_of_injective
+-/
 
 end GaloisCoinsertion
 
@@ -671,54 +773,72 @@ section GaloisInsertion
 
 variable {ι : Type _} {f : M →[L] N} (hf : Function.Surjective f)
 
-include hf
-
+#print FirstOrder.Language.Substructure.giMapComap /-
 /-- `map f` and `comap f` form a `galois_insertion` when `f` is surjective. -/
 def giMapComap : GaloisInsertion (map f) (comap f) :=
   (gc_map_comap f).toGaloisInsertion fun S x h =>
     let ⟨y, hy⟩ := hf x
     mem_map.2 ⟨y, by simp [hy, h]⟩
 #align first_order.language.substructure.gi_map_comap FirstOrder.Language.Substructure.giMapComap
+-/
 
+#print FirstOrder.Language.Substructure.map_comap_eq_of_surjective /-
 theorem map_comap_eq_of_surjective (S : L.Substructure N) : (S.comap f).map f = S :=
   (giMapComap hf).l_u_eq _
 #align first_order.language.substructure.map_comap_eq_of_surjective FirstOrder.Language.Substructure.map_comap_eq_of_surjective
+-/
 
+#print FirstOrder.Language.Substructure.map_surjective_of_surjective /-
 theorem map_surjective_of_surjective : Function.Surjective (map f) :=
   (giMapComap hf).l_surjective
 #align first_order.language.substructure.map_surjective_of_surjective FirstOrder.Language.Substructure.map_surjective_of_surjective
+-/
 
+#print FirstOrder.Language.Substructure.comap_injective_of_surjective /-
 theorem comap_injective_of_surjective : Function.Injective (comap f) :=
   (giMapComap hf).u_injective
 #align first_order.language.substructure.comap_injective_of_surjective FirstOrder.Language.Substructure.comap_injective_of_surjective
+-/
 
+#print FirstOrder.Language.Substructure.map_inf_comap_of_surjective /-
 theorem map_inf_comap_of_surjective (S T : L.Substructure N) :
     (S.comap f ⊓ T.comap f).map f = S ⊓ T :=
   (giMapComap hf).l_inf_u _ _
 #align first_order.language.substructure.map_inf_comap_of_surjective FirstOrder.Language.Substructure.map_inf_comap_of_surjective
+-/
 
+#print FirstOrder.Language.Substructure.map_iInf_comap_of_surjective /-
 theorem map_iInf_comap_of_surjective (S : ι → L.Substructure N) :
     (⨅ i, (S i).comap f).map f = iInf S :=
   (giMapComap hf).l_iInf_u _
 #align first_order.language.substructure.map_infi_comap_of_surjective FirstOrder.Language.Substructure.map_iInf_comap_of_surjective
+-/
 
+#print FirstOrder.Language.Substructure.map_sup_comap_of_surjective /-
 theorem map_sup_comap_of_surjective (S T : L.Substructure N) :
     (S.comap f ⊔ T.comap f).map f = S ⊔ T :=
   (giMapComap hf).l_sup_u _ _
 #align first_order.language.substructure.map_sup_comap_of_surjective FirstOrder.Language.Substructure.map_sup_comap_of_surjective
+-/
 
+#print FirstOrder.Language.Substructure.map_iSup_comap_of_surjective /-
 theorem map_iSup_comap_of_surjective (S : ι → L.Substructure N) :
     (⨆ i, (S i).comap f).map f = iSup S :=
   (giMapComap hf).l_iSup_u _
 #align first_order.language.substructure.map_supr_comap_of_surjective FirstOrder.Language.Substructure.map_iSup_comap_of_surjective
+-/
 
+#print FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjective /-
 theorem comap_le_comap_iff_of_surjective {S T : L.Substructure N} : S.comap f ≤ T.comap f ↔ S ≤ T :=
   (giMapComap hf).u_le_u_iff
 #align first_order.language.substructure.comap_le_comap_iff_of_surjective FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjective
+-/
 
+#print FirstOrder.Language.Substructure.comap_strictMono_of_surjective /-
 theorem comap_strictMono_of_surjective : StrictMono (comap f) :=
   (giMapComap hf).strictMono_u
 #align first_order.language.substructure.comap_strict_mono_of_surjective FirstOrder.Language.Substructure.comap_strictMono_of_surjective
+-/
 
 end GaloisInsertion
 
@@ -785,8 +905,7 @@ open Substructure
 
 variable {L' : Language} [L'.Structure M] (φ : L →ᴸ L') [φ.IsExpansionOn M]
 
-include φ
-
+#print FirstOrder.Language.LHom.substructureReduct /-
 /-- Reduces the language of a substructure along a language hom. -/
 def substructureReduct : L'.Substructure M ↪o L.Substructure M
     where
@@ -802,17 +921,22 @@ def substructureReduct : L'.Substructure M ↪o L.Substructure M
     exact h
   map_rel_iff' S T := Iff.rfl
 #align first_order.language.Lhom.substructure_reduct FirstOrder.Language.LHom.substructureReduct
+-/
 
+#print FirstOrder.Language.LHom.mem_substructureReduct /-
 @[simp]
 theorem mem_substructureReduct {x : M} {S : L'.Substructure M} :
     x ∈ φ.substructureReduct S ↔ x ∈ S :=
   Iff.rfl
 #align first_order.language.Lhom.mem_substructure_reduct FirstOrder.Language.LHom.mem_substructureReduct
+-/
 
+#print FirstOrder.Language.LHom.coe_substructureReduct /-
 @[simp]
 theorem coe_substructureReduct {S : L'.Substructure M} : (φ.substructureReduct S : Set M) = ↑S :=
   rfl
 #align first_order.language.Lhom.coe_substructure_reduct FirstOrder.Language.LHom.coe_substructureReduct
+-/
 
 end Lhom
 
@@ -848,10 +972,12 @@ theorem coe_withConstants : (S.withConstants h : Set M) = ↑S :=
 #align first_order.language.substructure.coe_with_constants FirstOrder.Language.Substructure.coe_withConstants
 -/
 
+#print FirstOrder.Language.Substructure.reduct_withConstants /-
 @[simp]
 theorem reduct_withConstants : (L.lhomWithConstants A).substructureReduct (S.withConstants h) = S :=
   by ext; simp
 #align first_order.language.substructure.reduct_with_constants FirstOrder.Language.Substructure.reduct_withConstants
+-/
 
 #print FirstOrder.Language.Substructure.subset_closure_withConstants /-
 theorem subset_closure_withConstants : A ⊆ closure (L[[A]]) s :=
@@ -863,6 +989,7 @@ theorem subset_closure_withConstants : A ⊆ closure (L[[A]]) s :=
 #align first_order.language.substructure.subset_closure_with_constants FirstOrder.Language.Substructure.subset_closure_withConstants
 -/
 
+#print FirstOrder.Language.Substructure.closure_withConstants_eq /-
 theorem closure_withConstants_eq :
     closure (L[[A]]) s =
       (closure L (A ∪ s)).withConstants ((A.subset_union_left s).trans subset_closure) :=
@@ -875,6 +1002,7 @@ theorem closure_withConstants_eq :
   · infer_instance
   · infer_instance
 #align first_order.language.substructure.closure_with_constants_eq FirstOrder.Language.Substructure.closure_withConstants_eq
+-/
 
 end Substructure
 
@@ -901,17 +1029,21 @@ def codRestrict (p : L.Substructure N) (f : M →[L] N) (h : ∀ c, f c ∈ p) :
 #align first_order.language.hom.cod_restrict FirstOrder.Language.Hom.codRestrict
 -/
 
+#print FirstOrder.Language.Hom.comp_codRestrict /-
 @[simp]
 theorem comp_codRestrict (f : M →[L] N) (g : N →[L] P) (p : L.Substructure P) (h : ∀ b, g b ∈ p) :
     ((codRestrict p g h).comp f : M →[L] p) = codRestrict p (g.comp f) fun b => h _ :=
   ext fun b => rfl
 #align first_order.language.hom.comp_cod_restrict FirstOrder.Language.Hom.comp_codRestrict
+-/
 
+#print FirstOrder.Language.Hom.subtype_comp_codRestrict /-
 @[simp]
 theorem subtype_comp_codRestrict (f : M →[L] N) (p : L.Substructure N) (h : ∀ b, f b ∈ p) :
     p.Subtype.toHom.comp (codRestrict p f h) = f :=
   ext fun b => rfl
 #align first_order.language.hom.subtype_comp_cod_restrict FirstOrder.Language.Hom.subtype_comp_codRestrict
+-/
 
 #print FirstOrder.Language.Hom.range /-
 /-- The range of a first-order hom `f : M → N` is a submodule of `N`.
@@ -921,21 +1053,29 @@ def range (f : M →[L] N) : L.Substructure N :=
 #align first_order.language.hom.range FirstOrder.Language.Hom.range
 -/
 
+#print FirstOrder.Language.Hom.range_coe /-
 theorem range_coe (f : M →[L] N) : (range f : Set N) = Set.range f :=
   rfl
 #align first_order.language.hom.range_coe FirstOrder.Language.Hom.range_coe
+-/
 
+#print FirstOrder.Language.Hom.mem_range /-
 @[simp]
 theorem mem_range {f : M →[L] N} {x} : x ∈ range f ↔ ∃ y, f y = x :=
   Iff.rfl
 #align first_order.language.hom.mem_range FirstOrder.Language.Hom.mem_range
+-/
 
+#print FirstOrder.Language.Hom.range_eq_map /-
 theorem range_eq_map (f : M →[L] N) : f.range = map f ⊤ := by ext; simp
 #align first_order.language.hom.range_eq_map FirstOrder.Language.Hom.range_eq_map
+-/
 
+#print FirstOrder.Language.Hom.mem_range_self /-
 theorem mem_range_self (f : M →[L] N) (x : M) : f x ∈ f.range :=
   ⟨x, rfl⟩
 #align first_order.language.hom.mem_range_self FirstOrder.Language.Hom.mem_range_self
+-/
 
 #print FirstOrder.Language.Hom.range_id /-
 @[simp]
@@ -944,25 +1084,35 @@ theorem range_id : range (id L M) = ⊤ :=
 #align first_order.language.hom.range_id FirstOrder.Language.Hom.range_id
 -/
 
+#print FirstOrder.Language.Hom.range_comp /-
 theorem range_comp (f : M →[L] N) (g : N →[L] P) : range (g.comp f : M →[L] P) = map g (range f) :=
   SetLike.coe_injective (Set.range_comp g f)
 #align first_order.language.hom.range_comp FirstOrder.Language.Hom.range_comp
+-/
 
+#print FirstOrder.Language.Hom.range_comp_le_range /-
 theorem range_comp_le_range (f : M →[L] N) (g : N →[L] P) : range (g.comp f : M →[L] P) ≤ range g :=
   SetLike.coe_mono (Set.range_comp_subset_range f g)
 #align first_order.language.hom.range_comp_le_range FirstOrder.Language.Hom.range_comp_le_range
+-/
 
+#print FirstOrder.Language.Hom.range_eq_top /-
 theorem range_eq_top {f : M →[L] N} : range f = ⊤ ↔ Function.Surjective f := by
   rw [SetLike.ext'_iff, range_coe, coe_top, Set.range_iff_surjective]
 #align first_order.language.hom.range_eq_top FirstOrder.Language.Hom.range_eq_top
+-/
 
+#print FirstOrder.Language.Hom.range_le_iff_comap /-
 theorem range_le_iff_comap {f : M →[L] N} {p : L.Substructure N} : range f ≤ p ↔ comap f p = ⊤ := by
   rw [range_eq_map, map_le_iff_le_comap, eq_top_iff]
 #align first_order.language.hom.range_le_iff_comap FirstOrder.Language.Hom.range_le_iff_comap
+-/
 
+#print FirstOrder.Language.Hom.map_le_range /-
 theorem map_le_range {f : M →[L] N} {p : L.Substructure M} : map f p ≤ range f :=
   SetLike.coe_mono (Set.image_subset_range f p)
 #align first_order.language.hom.map_le_range FirstOrder.Language.Hom.map_le_range
+-/
 
 #print FirstOrder.Language.Hom.eqLocus /-
 /-- The substructure of elements `x : M` such that `f x = g x` -/
@@ -976,21 +1126,27 @@ def eqLocus (f g : M →[L] N) : Substructure L M
 #align first_order.language.hom.eq_locus FirstOrder.Language.Hom.eqLocus
 -/
 
+#print FirstOrder.Language.Hom.eqOn_closure /-
 /-- If two `L.hom`s are equal on a set, then they are equal on its substructure closure. -/
 theorem eqOn_closure {f g : M →[L] N} {s : Set M} (h : Set.EqOn f g s) :
     Set.EqOn f g (closure L s) :=
   show closure L s ≤ f.eqLocus g from closure_le.2 h
 #align first_order.language.hom.eq_on_closure FirstOrder.Language.Hom.eqOn_closure
+-/
 
+#print FirstOrder.Language.Hom.eq_of_eqOn_top /-
 theorem eq_of_eqOn_top {f g : M →[L] N} (h : Set.EqOn f g (⊤ : Substructure L M)) : f = g :=
   ext fun x => h trivial
 #align first_order.language.hom.eq_of_eq_on_top FirstOrder.Language.Hom.eq_of_eqOn_top
+-/
 
 variable {s : Set M}
 
+#print FirstOrder.Language.Hom.eq_of_eqOn_dense /-
 theorem eq_of_eqOn_dense (hs : closure L s = ⊤) {f g : M →[L] N} (h : s.EqOn f g) : f = g :=
   eq_of_eqOn_top <| hs ▸ eqOn_closure h
 #align first_order.language.hom.eq_of_eq_on_dense FirstOrder.Language.Hom.eq_of_eqOn_dense
+-/
 
 end Hom
 
@@ -1006,10 +1162,12 @@ def domRestrict (f : M ↪[L] N) (p : L.Substructure M) : p ↪[L] N :=
 #align first_order.language.embedding.dom_restrict FirstOrder.Language.Embedding.domRestrict
 -/
 
+#print FirstOrder.Language.Embedding.domRestrict_apply /-
 @[simp]
 theorem domRestrict_apply (f : M ↪[L] N) (p : L.Substructure M) (x : p) : f.domRestrict p x = f x :=
   rfl
 #align first_order.language.embedding.dom_restrict_apply FirstOrder.Language.Embedding.domRestrict_apply
+-/
 
 #print FirstOrder.Language.Embedding.codRestrict /-
 /-- A first-order embedding `f : M → N` whose values lie in a substructure `p ⊆ N` can be restricted
@@ -1028,23 +1186,29 @@ def codRestrict (p : L.Substructure N) (f : M ↪[L] N) (h : ∀ c, f c ∈ p) :
 #align first_order.language.embedding.cod_restrict FirstOrder.Language.Embedding.codRestrict
 -/
 
+#print FirstOrder.Language.Embedding.codRestrict_apply /-
 @[simp]
 theorem codRestrict_apply (p : L.Substructure N) (f : M ↪[L] N) {h} (x : M) :
     (codRestrict p f h x : N) = f x :=
   rfl
 #align first_order.language.embedding.cod_restrict_apply FirstOrder.Language.Embedding.codRestrict_apply
+-/
 
+#print FirstOrder.Language.Embedding.comp_codRestrict /-
 @[simp]
 theorem comp_codRestrict (f : M ↪[L] N) (g : N ↪[L] P) (p : L.Substructure P) (h : ∀ b, g b ∈ p) :
     ((codRestrict p g h).comp f : M ↪[L] p) = codRestrict p (g.comp f) fun b => h _ :=
   ext fun b => rfl
 #align first_order.language.embedding.comp_cod_restrict FirstOrder.Language.Embedding.comp_codRestrict
+-/
 
+#print FirstOrder.Language.Embedding.subtype_comp_codRestrict /-
 @[simp]
 theorem subtype_comp_codRestrict (f : M ↪[L] N) (p : L.Substructure N) (h : ∀ b, f b ∈ p) :
     p.Subtype.comp (codRestrict p f h) = f :=
   ext fun b => rfl
 #align first_order.language.embedding.subtype_comp_cod_restrict FirstOrder.Language.Embedding.subtype_comp_codRestrict
+-/
 
 #print FirstOrder.Language.Embedding.substructureEquivMap /-
 /-- The equivalence between a substructure `s` and its image `s.map f.to_hom`, where `f` is an
@@ -1063,11 +1227,13 @@ noncomputable def substructureEquivMap (f : M ↪[L] N) (s : L.Substructure M) :
 #align first_order.language.embedding.substructure_equiv_map FirstOrder.Language.Embedding.substructureEquivMap
 -/
 
+#print FirstOrder.Language.Embedding.substructureEquivMap_apply /-
 @[simp]
 theorem substructureEquivMap_apply (f : M ↪[L] N) (p : L.Substructure M) (x : p) :
     (f.substructureEquivMap p x : N) = f x :=
   rfl
 #align first_order.language.embedding.substructure_equiv_map_apply FirstOrder.Language.Embedding.substructureEquivMap_apply
+-/
 
 #print FirstOrder.Language.Embedding.equivRange /-
 /-- The equivalence between the domain and the range of an embedding `f`. -/
@@ -1081,36 +1247,44 @@ noncomputable def equivRange (f : M ↪[L] N) : M ≃[L] f.toHom.range
 #align first_order.language.embedding.equiv_range FirstOrder.Language.Embedding.equivRange
 -/
 
+#print FirstOrder.Language.Embedding.equivRange_apply /-
 @[simp]
 theorem equivRange_apply (f : M ↪[L] N) (x : M) : (f.equivRange x : N) = f x :=
   rfl
 #align first_order.language.embedding.equiv_range_apply FirstOrder.Language.Embedding.equivRange_apply
+-/
 
 end Embedding
 
 namespace Equiv
 
+#print FirstOrder.Language.Equiv.toHom_range /-
 theorem toHom_range (f : M ≃[L] N) : f.toHom.range = ⊤ :=
   by
   ext n
   simp only [hom.mem_range, coe_to_hom, substructure.mem_top, iff_true_iff]
   exact ⟨f.symm n, apply_symm_apply _ _⟩
 #align first_order.language.equiv.to_hom_range FirstOrder.Language.Equiv.toHom_range
+-/
 
 end Equiv
 
 namespace Substructure
 
+#print FirstOrder.Language.Substructure.inclusion /-
 /-- The embedding associated to an inclusion of substructures. -/
 def inclusion {S T : L.Substructure M} (h : S ≤ T) : S ↪[L] T :=
   S.Subtype.codRestrict _ fun x => h x.2
 #align first_order.language.substructure.inclusion FirstOrder.Language.Substructure.inclusion
+-/
 
+#print FirstOrder.Language.Substructure.coe_inclusion /-
 @[simp]
 theorem coe_inclusion {S T : L.Substructure M} (h : S ≤ T) :
     (inclusion h : S → T) = Set.inclusion h :=
   rfl
 #align first_order.language.substructure.coe_inclusion FirstOrder.Language.Substructure.coe_inclusion
+-/
 
 #print FirstOrder.Language.Substructure.range_subtype /-
 theorem range_subtype (S : L.Substructure M) : S.Subtype.toHom.range = S :=

6cf59007

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -276,7 +276,7 @@ variable (L)
 
 /-- The `L.substructure` generated by a set. -/
 def closure : LowerAdjoint (coe : L.Substructure M → Set M) :=
-  ⟨fun s => sInf { S | s ⊆ S }, fun s S =>
+  ⟨fun s => sInf {S | s ⊆ S}, fun s S =>
     ⟨Set.Subset.trans fun x hx => mem_sInf.2 fun S hS => hS hx, fun h => sInf_le h⟩⟩
 #align first_order.language.substructure.closure FirstOrder.Language.Substructure.closure
 
@@ -769,7 +769,7 @@ theorem coe_topEquiv : ⇑(topEquiv : (⊤ : L.Substructure M) ≃[L] M) = coe :
 @[elab_as_elim]
 theorem closure_induction' (s : Set M) {p : ∀ x, x ∈ closure L s → Prop}
     (Hs : ∀ (x) (h : x ∈ s), p x (subset_closure h))
-    (Hfun : ∀ {n : ℕ} (f : L.Functions n), ClosedUnder f { x | ∃ hx, p x hx }) {x}
+    (Hfun : ∀ {n : ℕ} (f : L.Functions n), ClosedUnder f {x | ∃ hx, p x hx}) {x}
     (hx : x ∈ closure L s) : p x hx :=
   by
   refine' Exists.elim _ fun (hx : x ∈ closure L s) (hc : p x hx) => hc
@@ -968,7 +968,7 @@ theorem map_le_range {f : M →[L] N} {p : L.Substructure M} : map f p ≤ range
 /-- The substructure of elements `x : M` such that `f x = g x` -/
 def eqLocus (f g : M →[L] N) : Substructure L M
     where
-  carrier := { x : M | f x = g x }
+  carrier := {x : M | f x = g x}
   fun_mem n fn x hx :=
     by
     have h : f ∘ x = g ∘ x := by ext; repeat' rw [Function.comp_apply]; apply hx

6cf59007

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -117,7 +117,7 @@ variable {L} {M}
 namespace Substructure
 
 instance : SetLike (L.Substructure M) M :=
-  ⟨Substructure.carrier, fun p q h => by cases p <;> cases q <;> congr ⟩
+  ⟨Substructure.carrier, fun p q h => by cases p <;> cases q <;> congr⟩
 
 #print FirstOrder.Language.Substructure.Simps.coe /-
 /-- See Note [custom simps projection] -/
@@ -369,7 +369,7 @@ theorem lift_card_closure_le_card_term : Cardinal.lift.{max u w} (#closure L s)
 
 theorem lift_card_closure_le :
     Cardinal.lift.{u, w} (#closure L s) ≤
-      max ℵ₀ (Cardinal.lift.{u, w} (#s) + Cardinal.lift.{w, u} (#Σi, L.Functions i)) :=
+      max ℵ₀ (Cardinal.lift.{u, w} (#s) + Cardinal.lift.{w, u} (#Σ i, L.Functions i)) :=
   by
   rw [← lift_umax]
   refine' lift_card_closure_le_card_term.trans (term.card_le.trans _)
@@ -379,7 +379,7 @@ theorem lift_card_closure_le :
 variable (L)
 
 #print Set.Countable.substructure_closure /-
-theorem Set.Countable.substructure_closure [Countable (Σl, L.Functions l)] (h : s.Countable) :
+theorem Set.Countable.substructure_closure [Countable (Σ l, L.Functions l)] (h : s.Countable) :
     Countable.{w + 1} (closure L s) :=
   by
   haveI : Countable s := h.to_subtype
@@ -795,10 +795,10 @@ def substructureReduct : L'.Substructure M ↪o L.Substructure M
       fun_mem := fun n f x hx =>
         by
         have h := S.fun_mem (φ.on_function f) x hx
-        simp only [Lhom.map_on_function, substructure.mem_carrier] at h
+        simp only [Lhom.map_on_function, substructure.mem_carrier] at h 
         exact h }
   inj' S T h := by
-    simp only [SetLike.coe_set_eq] at h
+    simp only [SetLike.coe_set_eq] at h 
     exact h
   map_rel_iff' S T := Iff.rfl
 #align first_order.language.Lhom.substructure_reduct FirstOrder.Language.LHom.substructureReduct

6cf59007

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -53,7 +53,7 @@ variable {L : Language.{u, v}} {M : Type w} {N P : Type _}
 
 variable [L.Structure M] [L.Structure N] [L.Structure P]
 
-open FirstOrder Cardinal
+open scoped FirstOrder Cardinal
 
 open Structure Cardinal

6cf59007

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -82,22 +82,10 @@ variable {L f s} {t : Set M}
 
 namespace ClosedUnder
 
-/- warning: first_order.language.closed_under.inter -> FirstOrder.Language.ClosedUnder.inter is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {n : Nat} {f : FirstOrder.Language.Functions.{u1, u2} L n} {s : Set.{u3} M} {t : Set.{u3} M}, (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f s) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f t) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f (Inter.inter.{u3} (Set.{u3} M) (Set.hasInter.{u3} M) s t))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {n : Nat} {f : FirstOrder.Language.Functions.{u1, u2} L n} {s : Set.{u3} M} {t : Set.{u3} M}, (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f s) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f t) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f (Inter.inter.{u3} (Set.{u3} M) (Set.instInterSet.{u3} M) s t))
-Case conversion may be inaccurate. Consider using '#align first_order.language.closed_under.inter FirstOrder.Language.ClosedUnder.interₓ'. -/
 theorem inter (hs : ClosedUnder f s) (ht : ClosedUnder f t) : ClosedUnder f (s ∩ t) := fun x h =>
   mem_inter (hs x fun i => mem_of_mem_inter_left (h i)) (ht x fun i => mem_of_mem_inter_right (h i))
 #align first_order.language.closed_under.inter FirstOrder.Language.ClosedUnder.inter
 
-/- warning: first_order.language.closed_under.inf -> FirstOrder.Language.ClosedUnder.inf is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {n : Nat} {f : FirstOrder.Language.Functions.{u1, u2} L n} {s : Set.{u3} M} {t : Set.{u3} M}, (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f s) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f t) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f (Inf.inf.{u3} (Set.{u3} M) (SemilatticeInf.toHasInf.{u3} (Set.{u3} M) (Lattice.toSemilatticeInf.{u3} (Set.{u3} M) (ConditionallyCompleteLattice.toLattice.{u3} (Set.{u3} M) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M)))))))) s t))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {n : Nat} {f : FirstOrder.Language.Functions.{u1, u2} L n} {s : Set.{u3} M} {t : Set.{u3} M}, (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f s) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f t) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f (Inf.inf.{u3} (Set.{u3} M) (Lattice.toInf.{u3} (Set.{u3} M) (ConditionallyCompleteLattice.toLattice.{u3} (Set.{u3} M) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) s t))
-Case conversion may be inaccurate. Consider using '#align first_order.language.closed_under.inf FirstOrder.Language.ClosedUnder.infₓ'. -/
 theorem inf (hs : ClosedUnder f s) (ht : ClosedUnder f t) : ClosedUnder f (s ⊓ t) :=
   hs.inter ht
 #align first_order.language.closed_under.inf FirstOrder.Language.ClosedUnder.inf
@@ -168,12 +156,6 @@ end Substructure
 
 variable {S : L.Substructure M}
 
-/- warning: first_order.language.term.realize_mem -> FirstOrder.Language.Term.realize_mem is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {α : Type.{u4}} (t : FirstOrder.Language.Term.{u1, u2, u4} L α) (xs : α -> M), (forall (a : α), Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (xs a) S) -> (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Term.realize.{u1, u2, u3, u4} L M _inst_1 α xs t) S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {α : Type.{u1}} (t : FirstOrder.Language.Term.{u2, u3, u1} L α) (xs : α -> M), (forall (a : α), Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (xs a) S) -> (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Term.realize.{u2, u3, u4, u1} L M _inst_1 α xs t) S)
-Case conversion may be inaccurate. Consider using '#align first_order.language.term.realize_mem FirstOrder.Language.Term.realize_memₓ'. -/
 theorem Term.realize_mem {α : Type _} (t : L.term α) (xs : α → M) (h : ∀ a, xs a ∈ S) :
     t.realize xs ∈ S := by
   induction' t with a n f ts ih
@@ -196,12 +178,6 @@ theorem copy_eq {s : Set M} (hs : s = S) : S.copy s hs = S :=
 #align first_order.language.substructure.copy_eq FirstOrder.Language.Substructure.copy_eq
 -/
 
-/- warning: first_order.language.substructure.constants_mem -> FirstOrder.Language.Substructure.constants_mem is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} (c : FirstOrder.Language.Constants.{u1, u2} L), Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u3}) [self : HasLiftT.{succ u1, succ u3} a b] => self.0) (FirstOrder.Language.Constants.{u1, u2} L) M (HasLiftT.mk.{succ u1, succ u3} (FirstOrder.Language.Constants.{u1, u2} L) M (CoeTCₓ.coe.{succ u1, succ u3} (FirstOrder.Language.Constants.{u1, u2} L) M (FirstOrder.Language.hasCoeT.{u1, u2, u3} L M _inst_1))) c) S
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} (c : FirstOrder.Language.Constants.{u1, u2} L), Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.constantMap.{u1, u2, u3} L M _inst_1 c) S
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.constants_mem FirstOrder.Language.Substructure.constants_memₓ'. -/
 theorem constants_mem (c : L.Constants) : ↑c ∈ S :=
   mem_carrier.2 (S.fun_mem c _ Fin.elim0)
 #align first_order.language.substructure.constants_mem FirstOrder.Language.Substructure.constants_mem
@@ -234,12 +210,6 @@ instance : Inf (L.Substructure M) :=
     { carrier := S₁ ∩ S₂
       fun_mem := fun n f => (S₁.fun_mem f).inf (S₂.fun_mem f) }⟩
 
-/- warning: first_order.language.substructure.coe_inf -> FirstOrder.Language.Substructure.coe_inf is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] (p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (p' : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1), Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (Inf.inf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u1, u2, u3} L M _inst_1) p p')) (Inter.inter.{u3} (Set.{u3} M) (Set.hasInter.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) p) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) p'))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] (p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (p' : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) (Inf.inf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u1, u2, u3} L M _inst_1) p p')) (Inter.inter.{u3} (Set.{u3} M) (Set.instInterSet.{u3} M) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) p) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) p'))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.coe_inf FirstOrder.Language.Substructure.coe_infₓ'. -/
 @[simp]
 theorem coe_inf (p p' : L.Substructure M) : ((p ⊓ p' : L.Substructure M) : Set M) = p ∩ p' :=
   rfl
@@ -277,22 +247,10 @@ theorem mem_sInf {S : Set (L.Substructure M)} {x : M} : x ∈ sInf S ↔ ∀ p 
 #align first_order.language.substructure.mem_Inf FirstOrder.Language.Substructure.mem_sInf
 -/
 
-/- warning: first_order.language.substructure.mem_infi -> FirstOrder.Language.Substructure.mem_iInf is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} {S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)} {x : M}, Iff (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (iInf.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (S i))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} {S : ι -> (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1)} {x : M}, Iff (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x (iInf.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u2, u3, u4} L M _inst_1) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x (S i))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_iInfₓ'. -/
 theorem mem_iInf {ι : Sort _} {S : ι → L.Substructure M} {x : M} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i :=
   by simp only [iInf, mem_Inf, Set.forall_range_iff]
 #align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_iInf
 
-/- warning: first_order.language.substructure.coe_infi -> FirstOrder.Language.Substructure.coe_iInf is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} {S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)}, Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (iInf.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => S i))) (Set.iInter.{u3, u4} M ι (fun (i : ι) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (S i)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} {S : ι -> (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1)}, Eq.{succ u4} (Set.{u4} M) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (iInf.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u2, u3, u4} L M _inst_1) ι (fun (i : ι) => S i))) (Set.iInter.{u4, u1} M ι (fun (i : ι) => SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (S i)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.coe_infi FirstOrder.Language.Substructure.coe_iInfₓ'. -/
 @[simp, norm_cast]
 theorem coe_iInf {ι : Sort _} {S : ι → L.Substructure M} : (↑(⨅ i, S i) : Set M) = ⋂ i, S i := by
   simp only [iInf, coe_Inf, Set.biInter_range]
@@ -316,12 +274,6 @@ instance : CompleteLattice (L.Substructure M) :=
 
 variable (L)
 
-/- warning: first_order.language.substructure.closure -> FirstOrder.Language.Substructure.closure is a dubious translation:
-lean 3 declaration is
-  forall (L : FirstOrder.Language.{u1, u2}) {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))
-but is expected to have type
-  forall (L : FirstOrder.Language.{u1, u2}) {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure FirstOrder.Language.Substructure.closureₓ'. -/
 /-- The `L.substructure` generated by a set. -/
 def closure : LowerAdjoint (coe : L.Substructure M → Set M) :=
   ⟨fun s => sInf { S | s ⊆ S }, fun s S =>
@@ -359,30 +311,18 @@ theorem closed (S : L.Substructure M) : (closure L).closed (S : Set M) :=
 
 open Set
 
-/- warning: first_order.language.substructure.closure_le -> FirstOrder.Language.Substructure.closure_le is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, Iff (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S) (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, Iff (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S) (HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) s (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_le FirstOrder.Language.Substructure.closure_leₓ'. -/
 /-- A substructure `S` includes `closure L s` if and only if it includes `s`. -/
 @[simp]
 theorem closure_le : closure L s ≤ S ↔ s ⊆ S :=
   (closure L).closure_le_closed_iff_le s S.closed
 #align first_order.language.substructure.closure_le FirstOrder.Language.Substructure.closure_le
 
-/- warning: first_order.language.substructure.closure_mono -> FirstOrder.Language.Substructure.closure_mono is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_mono FirstOrder.Language.Substructure.closure_monoₓ'. -/
 /-- Substructure closure of a set is monotone in its argument: if `s ⊆ t`,
 then `closure L s ≤ closure L t`. -/
 theorem closure_mono ⦃s t : Set M⦄ (h : s ⊆ t) : closure L s ≤ closure L t :=
   (closure L).Monotone h
 #align first_order.language.substructure.closure_mono FirstOrder.Language.Substructure.closure_mono
 
-/- warning: first_order.language.substructure.closure_eq_of_le -> FirstOrder.Language.Substructure.closure_eq_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_eq_of_le FirstOrder.Language.Substructure.closure_eq_of_leₓ'. -/
 theorem closure_eq_of_le (h₁ : s ⊆ S) (h₂ : S ≤ closure L s) : closure L s = S :=
   (closure L).eq_of_le h₁ h₂
 #align first_order.language.substructure.closure_eq_of_le FirstOrder.Language.Substructure.closure_eq_of_le
@@ -427,12 +367,6 @@ theorem lift_card_closure_le_card_term : Cardinal.lift.{max u w} (#closure L s)
 #align first_order.language.substructure.lift_card_closure_le_card_term FirstOrder.Language.Substructure.lift_card_closure_le_card_term
 -/
 
-/- warning: first_order.language.substructure.lift_card_closure_le -> FirstOrder.Language.Substructure.lift_card_closure_le is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {s : Set.{u3} M}, LE.le.{succ (max u3 u1)} Cardinal.{max u3 u1} Cardinal.hasLe.{max u3 u1} (Cardinal.lift.{u1, u3} (Cardinal.mk.{u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)))) (LinearOrder.max.{succ (max u3 u1)} Cardinal.{max u3 u1} Cardinal.linearOrder.{max u3 u1} Cardinal.aleph0.{max u3 u1} (HAdd.hAdd.{succ (max u3 u1), succ (max u3 u1), succ (max u3 u1)} Cardinal.{max u3 u1} Cardinal.{max u3 u1} Cardinal.{max u3 u1} (instHAdd.{succ (max u3 u1)} Cardinal.{max u3 u1} Cardinal.hasAdd.{max u3 u1}) (Cardinal.lift.{u1, u3} (Cardinal.mk.{u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) s))) (Cardinal.lift.{u3, u1} (Cardinal.mk.{u1} (Sigma.{0, u1} Nat (fun (i : Nat) => FirstOrder.Language.Functions.{u1, u2} L i))))))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {s : Set.{u3} M}, LE.le.{max (succ u1) (succ u3)} Cardinal.{max u3 u1} Cardinal.instLECardinal.{max u1 u3} (Cardinal.lift.{u1, u3} (Cardinal.mk.{u3} (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s))))) (Max.max.{succ (max u1 u3)} Cardinal.{max u1 u3} (CanonicallyLinearOrderedAddMonoid.toMax.{max (succ u1) (succ u3)} Cardinal.{max u1 u3} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{max u1 u3}) Cardinal.aleph0.{max u1 u3} (HAdd.hAdd.{max (succ u1) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u3)} Cardinal.{max u3 u1} Cardinal.{max u1 u3} Cardinal.{max u3 u1} (instHAdd.{max (succ u1) (succ u3)} Cardinal.{max u3 u1} Cardinal.instAddCardinal.{max u1 u3}) (Cardinal.lift.{u1, u3} (Cardinal.mk.{u3} (Set.Elem.{u3} M s))) (Cardinal.lift.{u3, u1} (Cardinal.mk.{u1} (Sigma.{0, u1} Nat (fun (i : Nat) => FirstOrder.Language.Functions.{u1, u2} L i))))))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.lift_card_closure_le FirstOrder.Language.Substructure.lift_card_closure_leₓ'. -/
 theorem lift_card_closure_le :
     Cardinal.lift.{u, w} (#closure L s) ≤
       max ℵ₀ (Cardinal.lift.{u, w} (#s) + Cardinal.lift.{w, u} (#Σi, L.Functions i)) :=
@@ -481,12 +415,6 @@ theorem dense_induction {p : M → Prop} (x : M) {s : Set M} (hs : closure L s =
 
 variable (L) (M)
 
-/- warning: first_order.language.substructure.gi -> FirstOrder.Language.Substructure.gi is a dubious translation:
-lean 3 declaration is
-  forall (L : FirstOrder.Language.{u1, u2}) (M : Type.{u3}) [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], GaloisInsertion.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))
-but is expected to have type
-  forall (L : FirstOrder.Language.{u1, u2}) (M : Type.{u3}) [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], GaloisInsertion.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1)) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.gi FirstOrder.Language.Substructure.giₓ'. -/
 /-- `closure` forms a Galois insertion with the coercion to set. -/
 protected def gi : GaloisInsertion (@closure L M _) coe
     where
@@ -506,12 +434,6 @@ theorem closure_eq : closure L (S : Set M) = S :=
 #align first_order.language.substructure.closure_eq FirstOrder.Language.Substructure.closure_eq
 -/
 
-/- warning: first_order.language.substructure.closure_empty -> FirstOrder.Language.Substructure.closure_empty is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (EmptyCollection.emptyCollection.{u3} (Set.{u3} M) (Set.hasEmptyc.{u3} M))) (Bot.bot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toHasBot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (EmptyCollection.emptyCollection.{u3} (Set.{u3} M) (Set.instEmptyCollectionSet.{u3} M))) (Bot.bot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toBot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_empty FirstOrder.Language.Substructure.closure_emptyₓ'. -/
 @[simp]
 theorem closure_empty : closure L (∅ : Set M) = ⊥ :=
   (Substructure.gi L M).gc.l_bot
@@ -524,26 +446,14 @@ theorem closure_univ : closure L (univ : Set M) = ⊤ :=
 #align first_order.language.substructure.closure_univ FirstOrder.Language.Substructure.closure_univ
 -/
 
-/- warning: first_order.language.substructure.closure_union -> FirstOrder.Language.Substructure.closure_union is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_union FirstOrder.Language.Substructure.closure_unionₓ'. -/
 theorem closure_union (s t : Set M) : closure L (s ∪ t) = closure L s ⊔ closure L t :=
   (Substructure.gi L M).gc.l_sup
 #align first_order.language.substructure.closure_union FirstOrder.Language.Substructure.closure_union
 
-/- warning: first_order.language.substructure.closure_Union -> FirstOrder.Language.Substructure.closure_unionᵢ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_Union FirstOrder.Language.Substructure.closure_unionᵢₓ'. -/
 theorem closure_unionᵢ {ι} (s : ι → Set M) : closure L (⋃ i, s i) = ⨆ i, closure L (s i) :=
   (Substructure.gi L M).gc.l_iSup
 #align first_order.language.substructure.closure_Union FirstOrder.Language.Substructure.closure_unionᵢ
 
-/- warning: first_order.language.substructure.small_bot -> FirstOrder.Language.Substructure.small_bot is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], Small.{u1, u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (Bot.bot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toHasBot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], Small.{u1, u3} (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (Bot.bot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toBot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.small_bot FirstOrder.Language.Substructure.small_botₓ'. -/
 instance small_bot : Small.{u} (⊥ : L.Substructure M) :=
   by
   rw [← closure_empty]
@@ -567,34 +477,16 @@ def comap (φ : M →[L] N) (S : L.Substructure N) : L.Substructure M
 #align first_order.language.substructure.comap FirstOrder.Language.Substructure.comap
 -/
 
-/- warning: first_order.language.substructure.mem_comap -> FirstOrder.Language.Substructure.mem_comap is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {x : M}, Iff (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) (Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x) S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {x : M}, Iff (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)) (Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) x) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f x) S)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.mem_comap FirstOrder.Language.Substructure.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap {S : L.Substructure N} {f : M →[L] N} {x : M} : x ∈ S.comap f ↔ f x ∈ S :=
   Iff.rfl
 #align first_order.language.substructure.mem_comap FirstOrder.Language.Substructure.mem_comap
 
-/- warning: first_order.language.substructure.comap_comap -> FirstOrder.Language.Substructure.comap_comap is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (S : FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u4, u5} L N P _inst_2 _inst_3 g S)) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u5} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f) S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u1} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u2} L P] (S : FirstOrder.Language.Substructure.{u3, u4, u2} L P _inst_3) (g : FirstOrder.Language.Hom.{u3, u4, u1, u2} L N P _inst_2 _inst_3) (f : FirstOrder.Language.Hom.{u3, u4, u5, u1} L M N _inst_1 _inst_2), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u3, u4, u1, u2} L N P _inst_2 _inst_3 g S)) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u3, u4, u5, u1, u2} L M N _inst_1 _inst_2 P _inst_3 g f) S)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_comap FirstOrder.Language.Substructure.comap_comapₓ'. -/
 theorem comap_comap (S : L.Substructure P) (g : N →[L] P) (f : M →[L] N) :
     (S.comap g).comap f = S.comap (g.comp f) :=
   rfl
 #align first_order.language.substructure.comap_comap FirstOrder.Language.Substructure.comap_comap
 
-/- warning: first_order.language.substructure.comap_id -> FirstOrder.Language.Substructure.comap_id is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {P : Type.{u3}} [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u3} L P] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L P _inst_3), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L P _inst_3) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u3} L P P _inst_3 _inst_3 (FirstOrder.Language.Hom.id.{u1, u2, u3} L P _inst_3) S) S
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {P : Type.{u1}} [_inst_3 : FirstOrder.Language.Structure.{u2, u3, u1} L P] (S : FirstOrder.Language.Substructure.{u2, u3, u1} L P _inst_3), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L P _inst_3) (FirstOrder.Language.Substructure.comap.{u2, u3, u1, u1} L P P _inst_3 _inst_3 (FirstOrder.Language.Hom.id.{u2, u3, u1} L P _inst_3) S) S
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_id FirstOrder.Language.Substructure.comap_idₓ'. -/
 @[simp]
 theorem comap_id (S : L.Substructure P) : S.comap (Hom.id _ _) = S :=
   ext (by simp)
@@ -616,211 +508,91 @@ def map (φ : M →[L] N) (S : L.Substructure M) : L.Substructure N
 #align first_order.language.substructure.map FirstOrder.Language.Substructure.map
 -/
 
-/- warning: first_order.language.substructure.mem_map -> FirstOrder.Language.Substructure.mem_map is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {y : N}, Iff (Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) y (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) (Exists.{succ u3} M (fun (x : M) => Exists.{0} (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S) (fun (H : Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S) => Eq.{succ u4} N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x) y)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {y : N}, Iff (Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) y (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)) (Exists.{succ u4} M (fun (x : M) => And (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x S) (Eq.{succ u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (a : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) a) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f x) y)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.mem_map FirstOrder.Language.Substructure.mem_mapₓ'. -/
 @[simp]
 theorem mem_map {f : M →[L] N} {S : L.Substructure M} {y : N} : y ∈ S.map f ↔ ∃ x ∈ S, f x = y :=
   mem_image_iff_bex
 #align first_order.language.substructure.mem_map FirstOrder.Language.Substructure.mem_map
 
-/- warning: first_order.language.substructure.mem_map_of_mem -> FirstOrder.Language.Substructure.mem_map_of_mem is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {x : M}, (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S) -> (Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {x : M}, (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x S) -> (Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) x) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f x) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.mem_map_of_mem FirstOrder.Language.Substructure.mem_map_of_memₓ'. -/
 theorem mem_map_of_mem (f : M →[L] N) {S : L.Substructure M} {x : M} (hx : x ∈ S) : f x ∈ S.map f :=
   mem_image_of_mem f hx
 #align first_order.language.substructure.mem_map_of_mem FirstOrder.Language.Substructure.mem_map_of_mem
 
-/- warning: first_order.language.substructure.apply_coe_mem_map -> FirstOrder.Language.Substructure.apply_coe_mem_map is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x : coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S), Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) M (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) M (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) M (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) M (coeSubtype.{succ u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S))))) x)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (x : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x S)), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) (Subtype.val.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Set.{u4} M) (Set.instMembershipSet.{u4} M) x (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) S)) x)) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f (Subtype.val.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Set.{u4} M) (Set.instMembershipSet.{u4} M) x (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) S)) x)) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.apply_coe_mem_map FirstOrder.Language.Substructure.apply_coe_mem_mapₓ'. -/
 theorem apply_coe_mem_map (f : M →[L] N) (S : L.Substructure M) (x : S) : f x ∈ S.map f :=
   mem_map_of_mem f x.Prop
 #align first_order.language.substructure.apply_coe_mem_map FirstOrder.Language.Substructure.apply_coe_mem_map
 
-/- warning: first_order.language.substructure.map_map -> FirstOrder.Language.Substructure.map_map is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (FirstOrder.Language.Substructure.map.{u1, u2, u4, u5} L N P _inst_2 _inst_3 g (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u5} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f) S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} {P : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u1} L P] (S : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (g : FirstOrder.Language.Hom.{u3, u4, u2, u1} L N P _inst_2 _inst_3) (f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (FirstOrder.Language.Substructure.map.{u3, u4, u2, u1} L N P _inst_2 _inst_3 g (FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f S)) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u1} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 P _inst_3 g f) S)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_map FirstOrder.Language.Substructure.map_mapₓ'. -/
 theorem map_map (g : N →[L] P) (f : M →[L] N) : (S.map f).map g = S.map (g.comp f) :=
   SetLike.coe_injective <| image_image _ _ _
 #align first_order.language.substructure.map_map FirstOrder.Language.Substructure.map_map
 
-/- warning: first_order.language.substructure.map_le_iff_le_comap -> FirstOrder.Language.Substructure.map_le_iff_le_comap is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2}, Iff (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) T) (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_le_iff_le_comap FirstOrder.Language.Substructure.map_le_iff_le_comapₓ'. -/
 theorem map_le_iff_le_comap {f : M →[L] N} {S : L.Substructure M} {T : L.Substructure N} :
     S.map f ≤ T ↔ S ≤ T.comap f :=
   image_subset_iff
 #align first_order.language.substructure.map_le_iff_le_comap FirstOrder.Language.Substructure.map_le_iff_le_comap
 
-/- warning: first_order.language.substructure.gc_map_comap -> FirstOrder.Language.Substructure.gc_map_comap is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), GaloisConnection.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), GaloisConnection.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.gc_map_comap FirstOrder.Language.Substructure.gc_map_comapₓ'. -/
 theorem gc_map_comap (f : M →[L] N) : GaloisConnection (map f) (comap f) := fun S T =>
   map_le_iff_le_comap
 #align first_order.language.substructure.gc_map_comap FirstOrder.Language.Substructure.gc_map_comap
 
-/- warning: first_order.language.substructure.map_le_of_le_comap -> FirstOrder.Language.Substructure.map_le_of_le_comap is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) -> (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T)) -> (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) T)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_le_of_le_comap FirstOrder.Language.Substructure.map_le_of_le_comapₓ'. -/
 theorem map_le_of_le_comap {T : L.Substructure N} {f : M →[L] N} : S ≤ T.comap f → S.map f ≤ T :=
   (gc_map_comap f).l_le
 #align first_order.language.substructure.map_le_of_le_comap FirstOrder.Language.Substructure.map_le_of_le_comap
 
-/- warning: first_order.language.substructure.le_comap_of_map_le -> FirstOrder.Language.Substructure.le_comap_of_map_le is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) T) -> (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.le_comap_of_map_le FirstOrder.Language.Substructure.le_comap_of_map_leₓ'. -/
 theorem le_comap_of_map_le {T : L.Substructure N} {f : M →[L] N} : S.map f ≤ T → S ≤ T.comap f :=
   (gc_map_comap f).le_u
 #align first_order.language.substructure.le_comap_of_map_le FirstOrder.Language.Substructure.le_comap_of_map_le
 
-/- warning: first_order.language.substructure.le_comap_map -> FirstOrder.Language.Substructure.le_comap_map is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.le_comap_map FirstOrder.Language.Substructure.le_comap_mapₓ'. -/
 theorem le_comap_map {f : M →[L] N} : S ≤ (S.map f).comap f :=
   (gc_map_comap f).le_u_l _
 #align first_order.language.substructure.le_comap_map FirstOrder.Language.Substructure.le_comap_map
 
-/- warning: first_order.language.substructure.map_comap_le -> FirstOrder.Language.Substructure.map_comap_le is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) S
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)) S
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_comap_le FirstOrder.Language.Substructure.map_comap_leₓ'. -/
 theorem map_comap_le {S : L.Substructure N} {f : M →[L] N} : (S.comap f).map f ≤ S :=
   (gc_map_comap f).l_u_le _
 #align first_order.language.substructure.map_comap_le FirstOrder.Language.Substructure.map_comap_le
 
-/- warning: first_order.language.substructure.monotone_map -> FirstOrder.Language.Substructure.monotone_map is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, Monotone.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, Monotone.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.monotone_map FirstOrder.Language.Substructure.monotone_mapₓ'. -/
 theorem monotone_map {f : M →[L] N} : Monotone (map f) :=
   (gc_map_comap f).monotone_l
 #align first_order.language.substructure.monotone_map FirstOrder.Language.Substructure.monotone_map
 
-/- warning: first_order.language.substructure.monotone_comap -> FirstOrder.Language.Substructure.monotone_comap is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, Monotone.{u4, u3} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, Monotone.{u1, u4} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.monotone_comap FirstOrder.Language.Substructure.monotone_comapₓ'. -/
 theorem monotone_comap {f : M →[L] N} : Monotone (comap f) :=
   (gc_map_comap f).monotone_u
 #align first_order.language.substructure.monotone_comap FirstOrder.Language.Substructure.monotone_comap
 
-/- warning: first_order.language.substructure.map_comap_map -> FirstOrder.Language.Substructure.map_comap_map is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_comap_map FirstOrder.Language.Substructure.map_comap_mapₓ'. -/
 @[simp]
 theorem map_comap_map {f : M →[L] N} : ((S.map f).comap f).map f = S.map f :=
   (gc_map_comap f).l_u_l_eq_l _
 #align first_order.language.substructure.map_comap_map FirstOrder.Language.Substructure.map_comap_map
 
-/- warning: first_order.language.substructure.comap_map_comap -> FirstOrder.Language.Substructure.comap_map_comap is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S))) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_map_comap FirstOrder.Language.Substructure.comap_map_comapₓ'. -/
 @[simp]
 theorem comap_map_comap {S : L.Substructure N} {f : M →[L] N} :
     ((S.comap f).map f).comap f = S.comap f :=
   (gc_map_comap f).u_l_u_eq_u _
 #align first_order.language.substructure.comap_map_comap FirstOrder.Language.Substructure.comap_map_comap
 
-/- warning: first_order.language.substructure.map_sup -> FirstOrder.Language.Substructure.map_sup is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Sup.sup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SemilatticeSup.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Lattice.toSemilatticeSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S T)) (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SemilatticeSup.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (T : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SemilatticeSup.toSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S T)) (Sup.sup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SemilatticeSup.toSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Lattice.toSemilatticeSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_sup FirstOrder.Language.Substructure.map_supₓ'. -/
 theorem map_sup (S T : L.Substructure M) (f : M →[L] N) : (S ⊔ T).map f = S.map f ⊔ T.map f :=
   (gc_map_comap f).l_sup
 #align first_order.language.substructure.map_sup FirstOrder.Language.Substructure.map_sup
 
-/- warning: first_order.language.substructure.map_supr -> FirstOrder.Language.Substructure.map_iSup is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Sort.{u5}} (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iSup.{u3, u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι s)) (iSup.{u4, u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (s i)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u1} L N] {ι : Sort.{u2}} (f : FirstOrder.Language.Hom.{u3, u4, u5, u1} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (iSup.{u5, u2} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι s)) (iSup.{u1, u2} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u1} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (s i)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_iSupₓ'. -/
 theorem map_iSup {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure M) :
     (iSup s).map f = ⨆ i, (s i).map f :=
   (gc_map_comap f).l_iSup
 #align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_iSup
 
-/- warning: first_order.language.substructure.comap_inf -> FirstOrder.Language.Substructure.comap_inf is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u1, u2, u4} L N _inst_2) S T)) (Inf.inf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Inf.inf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u2, u3, u1} L N _inst_2) S T)) (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_inf FirstOrder.Language.Substructure.comap_infₓ'. -/
 theorem comap_inf (S T : L.Substructure N) (f : M →[L] N) :
     (S ⊓ T).comap f = S.comap f ⊓ T.comap f :=
   (gc_map_comap f).u_inf
 #align first_order.language.substructure.comap_inf FirstOrder.Language.Substructure.comap_inf
 
-/- warning: first_order.language.substructure.comap_infi -> FirstOrder.Language.Substructure.comap_iInf is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Sort.{u5}} (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iInf.{u4, u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι s)) (iInf.{u3, u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (s i)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u1} L N] {ι : Sort.{u2}} (f : FirstOrder.Language.Hom.{u3, u4, u5, u1} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (iInf.{u1, u2} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u1} L N _inst_2) ι s)) (iInf.{u5, u2} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (s i)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_iInfₓ'. -/
 theorem comap_iInf {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure N) :
     (iInf s).comap f = ⨅ i, (s i).comap f :=
   (gc_map_comap f).u_iInf
 #align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_iInf
 
-/- warning: first_order.language.substructure.map_bot -> FirstOrder.Language.Substructure.map_bot is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Bot.bot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toHasBot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (Bot.bot.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toHasBot.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Bot.bot.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toBot.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (Bot.bot.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toBot.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_bot FirstOrder.Language.Substructure.map_botₓ'. -/
 @[simp]
 theorem map_bot (f : M →[L] N) : (⊥ : L.Substructure M).map f = ⊥ :=
   (gc_map_comap f).l_bot
 #align first_order.language.substructure.map_bot FirstOrder.Language.Substructure.map_bot
 
-/- warning: first_order.language.substructure.comap_top -> FirstOrder.Language.Substructure.comap_top is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Top.top.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u1, u2, u4} L N _inst_2))) (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Top.top.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u2, u3, u1} L N _inst_2))) (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_top FirstOrder.Language.Substructure.comap_topₓ'. -/
 @[simp]
 theorem comap_top (f : M →[L] N) : (⊤ : L.Substructure N).comap f = ⊤ :=
   (gc_map_comap f).u_top
@@ -833,18 +605,12 @@ theorem map_id (S : L.Substructure M) : S.map (Hom.id L M) = S :=
 #align first_order.language.substructure.map_id FirstOrder.Language.Substructure.map_id
 -/
 
-/- warning: first_order.language.substructure.map_closure -> FirstOrder.Language.Substructure.map_closure is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_closure FirstOrder.Language.Substructure.map_closureₓ'. -/
 theorem map_closure (f : M →[L] N) (s : Set M) : (closure L s).map f = closure L (f '' s) :=
   Eq.symm <|
     closure_eq_of_le (Set.image_subset f subset_closure) <|
       map_le_iff_le_comap.2 <| closure_le.2 fun x hx => subset_closure ⟨x, hx, rfl⟩
 #align first_order.language.substructure.map_closure FirstOrder.Language.Substructure.map_closure
 
-/- warning: first_order.language.substructure.closure_image -> FirstOrder.Language.Substructure.closure_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_image FirstOrder.Language.Substructure.closure_imageₓ'. -/
 @[simp]
 theorem closure_image (f : M →[L] N) : closure L (f '' s) = map f (closure L s) :=
   (map_closure f s).symm
@@ -856,105 +622,45 @@ variable {ι : Type _} {f : M →[L] N} (hf : Function.Injective f)
 
 include hf
 
-/- warning: first_order.language.substructure.gci_map_comap -> FirstOrder.Language.Substructure.gciMapComap is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (GaloisCoinsertion.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (GaloisCoinsertion.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.gci_map_comap FirstOrder.Language.Substructure.gciMapComapₓ'. -/
 /-- `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. -/
 def gciMapComap : GaloisCoinsertion (map f) (comap f) :=
   (gc_map_comap f).toGaloisCoinsertion fun S x => by simp [mem_comap, mem_map, hf.eq_iff]
 #align first_order.language.substructure.gci_map_comap FirstOrder.Language.Substructure.gciMapComap
 
-/- warning: first_order.language.substructure.comap_map_eq_of_injective -> FirstOrder.Language.Substructure.comap_map_eq_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)) S)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_map_eq_of_injective FirstOrder.Language.Substructure.comap_map_eq_of_injectiveₓ'. -/
 theorem comap_map_eq_of_injective (S : L.Substructure M) : (S.map f).comap f = S :=
   (gciMapComap hf).u_l_eq _
 #align first_order.language.substructure.comap_map_eq_of_injective FirstOrder.Language.Substructure.comap_map_eq_of_injective
 
-/- warning: first_order.language.substructure.comap_surjective_of_injective -> FirstOrder.Language.Substructure.comap_surjective_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (Function.Surjective.{succ u4, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (Function.Surjective.{succ u1, succ u4} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_surjective_of_injective FirstOrder.Language.Substructure.comap_surjective_of_injectiveₓ'. -/
 theorem comap_surjective_of_injective : Function.Surjective (comap f) :=
   (gciMapComap hf).u_surjective
 #align first_order.language.substructure.comap_surjective_of_injective FirstOrder.Language.Substructure.comap_surjective_of_injective
 
-/- warning: first_order.language.substructure.map_injective_of_injective -> FirstOrder.Language.Substructure.map_injective_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (Function.Injective.{succ u3, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (Function.Injective.{succ u4, succ u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_injective_of_injective FirstOrder.Language.Substructure.map_injective_of_injectiveₓ'. -/
 theorem map_injective_of_injective : Function.Injective (map f) :=
   (gciMapComap hf).l_injective
 #align first_order.language.substructure.map_injective_of_injective FirstOrder.Language.Substructure.map_injective_of_injective
 
-/- warning: first_order.language.substructure.comap_inf_map_of_injective -> FirstOrder.Language.Substructure.comap_inf_map_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))) (Inf.inf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u1, u2, u3} L M _inst_1) S T))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (T : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Inf.inf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))) (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u2, u3, u4} L M _inst_1) S T))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_inf_map_of_injective FirstOrder.Language.Substructure.comap_inf_map_of_injectiveₓ'. -/
 theorem comap_inf_map_of_injective (S T : L.Substructure M) : (S.map f ⊓ T.map f).comap f = S ⊓ T :=
   (gciMapComap hf).u_inf_l _ _
 #align first_order.language.substructure.comap_inf_map_of_injective FirstOrder.Language.Substructure.comap_inf_map_of_injective
 
-/- warning: first_order.language.substructure.comap_infi_map_of_injective -> FirstOrder.Language.Substructure.comap_iInf_map_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iInf.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (iInf.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι S))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Injective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (iInf.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u2} L N _inst_2) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (iInf.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι S))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_infi_map_of_injective FirstOrder.Language.Substructure.comap_iInf_map_of_injectiveₓ'. -/
 theorem comap_iInf_map_of_injective (S : ι → L.Substructure M) :
     (⨅ i, (S i).map f).comap f = iInf S :=
   (gciMapComap hf).u_iInf_l _
 #align first_order.language.substructure.comap_infi_map_of_injective FirstOrder.Language.Substructure.comap_iInf_map_of_injective
 
-/- warning: first_order.language.substructure.comap_sup_map_of_injective -> FirstOrder.Language.Substructure.comap_sup_map_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SemilatticeSup.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))) (Sup.sup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SemilatticeSup.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Lattice.toSemilatticeSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S T))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (T : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Sup.sup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SemilatticeSup.toSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Lattice.toSemilatticeSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))) (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SemilatticeSup.toSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S T))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_sup_map_of_injective FirstOrder.Language.Substructure.comap_sup_map_of_injectiveₓ'. -/
 theorem comap_sup_map_of_injective (S T : L.Substructure M) : (S.map f ⊔ T.map f).comap f = S ⊔ T :=
   (gciMapComap hf).u_sup_l _ _
 #align first_order.language.substructure.comap_sup_map_of_injective FirstOrder.Language.Substructure.comap_sup_map_of_injective
 
-/- warning: first_order.language.substructure.comap_supr_map_of_injective -> FirstOrder.Language.Substructure.comap_iSup_map_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iSup.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (iSup.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι S))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Injective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (iSup.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u2} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (iSup.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι S))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_supr_map_of_injective FirstOrder.Language.Substructure.comap_iSup_map_of_injectiveₓ'. -/
 theorem comap_iSup_map_of_injective (S : ι → L.Substructure M) :
     (⨆ i, (S i).map f).comap f = iSup S :=
   (gciMapComap hf).u_iSup_l _
 #align first_order.language.substructure.comap_supr_map_of_injective FirstOrder.Language.Substructure.comap_iSup_map_of_injective
 
-/- warning: first_order.language.substructure.map_le_map_iff_of_injective -> FirstOrder.Language.Substructure.map_le_map_iff_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {T : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1}, Iff (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T)) (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S T))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_le_map_iff_of_injective FirstOrder.Language.Substructure.map_le_map_iff_of_injectiveₓ'. -/
 theorem map_le_map_iff_of_injective {S T : L.Substructure M} : S.map f ≤ T.map f ↔ S ≤ T :=
   (gciMapComap hf).l_le_l_iff
 #align first_order.language.substructure.map_le_map_iff_of_injective FirstOrder.Language.Substructure.map_le_map_iff_of_injective
 
-/- warning: first_order.language.substructure.map_strict_mono_of_injective -> FirstOrder.Language.Substructure.map_strictMono_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (StrictMono.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (StrictMono.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_strict_mono_of_injective FirstOrder.Language.Substructure.map_strictMono_of_injectiveₓ'. -/
 theorem map_strictMono_of_injective : StrictMono (map f) :=
   (gciMapComap hf).strictMono_l
 #align first_order.language.substructure.map_strict_mono_of_injective FirstOrder.Language.Substructure.map_strictMono_of_injective
@@ -967,12 +673,6 @@ variable {ι : Type _} {f : M →[L] N} (hf : Function.Surjective f)
 
 include hf
 
-/- warning: first_order.language.substructure.gi_map_comap -> FirstOrder.Language.Substructure.giMapComap is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (GaloisInsertion.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (GaloisInsertion.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.gi_map_comap FirstOrder.Language.Substructure.giMapComapₓ'. -/
 /-- `map f` and `comap f` form a `galois_insertion` when `f` is surjective. -/
 def giMapComap : GaloisInsertion (map f) (comap f) :=
   (gc_map_comap f).toGaloisInsertion fun S x h =>
@@ -980,96 +680,42 @@ def giMapComap : GaloisInsertion (map f) (comap f) :=
     mem_map.2 ⟨y, by simp [hy, h]⟩
 #align first_order.language.substructure.gi_map_comap FirstOrder.Language.Substructure.giMapComap
 
-/- warning: first_order.language.substructure.map_comap_eq_of_surjective -> FirstOrder.Language.Substructure.map_comap_eq_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)) S)
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_comap_eq_of_surjective FirstOrder.Language.Substructure.map_comap_eq_of_surjectiveₓ'. -/
 theorem map_comap_eq_of_surjective (S : L.Substructure N) : (S.comap f).map f = S :=
   (giMapComap hf).l_u_eq _
 #align first_order.language.substructure.map_comap_eq_of_surjective FirstOrder.Language.Substructure.map_comap_eq_of_surjective
 
-/- warning: first_order.language.substructure.map_surjective_of_surjective -> FirstOrder.Language.Substructure.map_surjective_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (Function.Surjective.{succ u3, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (Function.Surjective.{succ u4, succ u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_surjective_of_surjective FirstOrder.Language.Substructure.map_surjective_of_surjectiveₓ'. -/
 theorem map_surjective_of_surjective : Function.Surjective (map f) :=
   (giMapComap hf).l_surjective
 #align first_order.language.substructure.map_surjective_of_surjective FirstOrder.Language.Substructure.map_surjective_of_surjective
 
-/- warning: first_order.language.substructure.comap_injective_of_surjective -> FirstOrder.Language.Substructure.comap_injective_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (Function.Injective.{succ u4, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (Function.Injective.{succ u1, succ u4} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_injective_of_surjective FirstOrder.Language.Substructure.comap_injective_of_surjectiveₓ'. -/
 theorem comap_injective_of_surjective : Function.Injective (comap f) :=
   (giMapComap hf).u_injective
 #align first_order.language.substructure.comap_injective_of_surjective FirstOrder.Language.Substructure.comap_injective_of_surjective
 
-/- warning: first_order.language.substructure.map_inf_comap_of_surjective -> FirstOrder.Language.Substructure.map_inf_comap_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Inf.inf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))) (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u1, u2, u4} L N _inst_2) S T))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))) (Inf.inf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u2, u3, u1} L N _inst_2) S T))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_inf_comap_of_surjective FirstOrder.Language.Substructure.map_inf_comap_of_surjectiveₓ'. -/
 theorem map_inf_comap_of_surjective (S T : L.Substructure N) :
     (S.comap f ⊓ T.comap f).map f = S ⊓ T :=
   (giMapComap hf).l_inf_u _ _
 #align first_order.language.substructure.map_inf_comap_of_surjective FirstOrder.Language.Substructure.map_inf_comap_of_surjective
 
-/- warning: first_order.language.substructure.map_infi_comap_of_surjective -> FirstOrder.Language.Substructure.map_iInf_comap_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iInf.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (iInf.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι S))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2)), Eq.{succ u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (iInf.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (iInf.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u2} L N _inst_2) ι S))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_infi_comap_of_surjective FirstOrder.Language.Substructure.map_iInf_comap_of_surjectiveₓ'. -/
 theorem map_iInf_comap_of_surjective (S : ι → L.Substructure N) :
     (⨅ i, (S i).comap f).map f = iInf S :=
   (giMapComap hf).l_iInf_u _
 #align first_order.language.substructure.map_infi_comap_of_surjective FirstOrder.Language.Substructure.map_iInf_comap_of_surjective
 
-/- warning: first_order.language.substructure.map_sup_comap_of_surjective -> FirstOrder.Language.Substructure.map_sup_comap_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Sup.sup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SemilatticeSup.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Lattice.toSemilatticeSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))) (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SemilatticeSup.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))))) S T))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SemilatticeSup.toSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))) (Sup.sup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SemilatticeSup.toSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Lattice.toSemilatticeSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) S T))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_sup_comap_of_surjective FirstOrder.Language.Substructure.map_sup_comap_of_surjectiveₓ'. -/
 theorem map_sup_comap_of_surjective (S T : L.Substructure N) :
     (S.comap f ⊔ T.comap f).map f = S ⊔ T :=
   (giMapComap hf).l_sup_u _ _
 #align first_order.language.substructure.map_sup_comap_of_surjective FirstOrder.Language.Substructure.map_sup_comap_of_surjective
 
-/- warning: first_order.language.substructure.map_supr_comap_of_surjective -> FirstOrder.Language.Substructure.map_iSup_comap_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iSup.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (iSup.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι S))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2)), Eq.{succ u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (iSup.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (iSup.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u2} L N _inst_2))) ι S))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_supr_comap_of_surjective FirstOrder.Language.Substructure.map_iSup_comap_of_surjectiveₓ'. -/
 theorem map_iSup_comap_of_surjective (S : ι → L.Substructure N) :
     (⨆ i, (S i).comap f).map f = iSup S :=
   (giMapComap hf).l_iSup_u _
 #align first_order.language.substructure.map_supr_comap_of_surjective FirstOrder.Language.Substructure.map_iSup_comap_of_surjective
 
-/- warning: first_order.language.substructure.comap_le_comap_iff_of_surjective -> FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) S T))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T)) (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) S T))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_le_comap_iff_of_surjective FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjectiveₓ'. -/
 theorem comap_le_comap_iff_of_surjective {S T : L.Substructure N} : S.comap f ≤ T.comap f ↔ S ≤ T :=
   (giMapComap hf).u_le_u_iff
 #align first_order.language.substructure.comap_le_comap_iff_of_surjective FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjective
 
-/- warning: first_order.language.substructure.comap_strict_mono_of_surjective -> FirstOrder.Language.Substructure.comap_strictMono_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (StrictMono.{u4, u3} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (StrictMono.{u1, u4} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_strict_mono_of_surjective FirstOrder.Language.Substructure.comap_strictMono_of_surjectiveₓ'. -/
 theorem comap_strictMono_of_surjective : StrictMono (comap f) :=
   (giMapComap hf).strictMono_u
 #align first_order.language.substructure.comap_strict_mono_of_surjective FirstOrder.Language.Substructure.comap_strictMono_of_surjective
@@ -1141,12 +787,6 @@ variable {L' : Language} [L'.Structure M] (φ : L →ᴸ L') [φ.IsExpansionOn M
 
 include φ
 
-/- warning: first_order.language.Lhom.substructure_reduct -> FirstOrder.Language.LHom.substructureReduct is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4], OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4], OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u4, u5, u3} L' M _inst_4))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.substructure_reduct FirstOrder.Language.LHom.substructureReductₓ'. -/
 /-- Reduces the language of a substructure along a language hom. -/
 def substructureReduct : L'.Substructure M ↪o L.Substructure M
     where
@@ -1163,18 +803,12 @@ def substructureReduct : L'.Substructure M ↪o L.Substructure M
   map_rel_iff' S T := Iff.rfl
 #align first_order.language.Lhom.substructure_reduct FirstOrder.Language.LHom.substructureReduct
 
-/- warning: first_order.language.Lhom.mem_substructure_reduct -> FirstOrder.Language.LHom.mem_substructureReduct is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.mem_substructure_reduct FirstOrder.Language.LHom.mem_substructureReductₓ'. -/
 @[simp]
 theorem mem_substructureReduct {x : M} {S : L'.Substructure M} :
     x ∈ φ.substructureReduct S ↔ x ∈ S :=
   Iff.rfl
 #align first_order.language.Lhom.mem_substructure_reduct FirstOrder.Language.LHom.mem_substructureReduct
 
-/- warning: first_order.language.Lhom.coe_substructure_reduct -> FirstOrder.Language.LHom.coe_substructureReduct is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.coe_substructure_reduct FirstOrder.Language.LHom.coe_substructureReductₓ'. -/
 @[simp]
 theorem coe_substructureReduct {S : L'.Substructure M} : (φ.substructureReduct S : Set M) = ↑S :=
   rfl
@@ -1214,9 +848,6 @@ theorem coe_withConstants : (S.withConstants h : Set M) = ↑S :=
 #align first_order.language.substructure.coe_with_constants FirstOrder.Language.Substructure.coe_withConstants
 -/
 
-/- warning: first_order.language.substructure.reduct_with_constants -> FirstOrder.Language.Substructure.reduct_withConstants is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.reduct_with_constants FirstOrder.Language.Substructure.reduct_withConstantsₓ'. -/
 @[simp]
 theorem reduct_withConstants : (L.lhomWithConstants A).substructureReduct (S.withConstants h) = S :=
   by ext; simp
@@ -1232,9 +863,6 @@ theorem subset_closure_withConstants : A ⊆ closure (L[[A]]) s :=
 #align first_order.language.substructure.subset_closure_with_constants FirstOrder.Language.Substructure.subset_closure_withConstants
 -/
 
-/- warning: first_order.language.substructure.closure_with_constants_eq -> FirstOrder.Language.Substructure.closure_withConstants_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_with_constants_eq FirstOrder.Language.Substructure.closure_withConstants_eqₓ'. -/
 theorem closure_withConstants_eq :
     closure (L[[A]]) s =
       (closure L (A ∪ s)).withConstants ((A.subset_union_left s).trans subset_closure) :=
@@ -1273,24 +901,12 @@ def codRestrict (p : L.Substructure N) (f : M →[L] N) (h : ∀ c, f c ∈ p) :
 #align first_order.language.hom.cod_restrict FirstOrder.Language.Hom.codRestrict
 -/
 
-/- warning: first_order.language.hom.comp_cod_restrict -> FirstOrder.Language.Hom.comp_codRestrict is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (p : FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (h : forall (b : N), Membership.Mem.{u5, u5} P (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (SetLike.hasMem.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) (coeFn.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3) => N -> P) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u4, u5} L N P _inst_2 _inst_3) g b) p), Eq.{max (succ u3) (succ u5)} (FirstOrder.Language.Hom.{u1, u2, u3, u5} L M (coeSort.{succ u5, succ (succ u5)} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u5} L P _inst_3 p)) (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 (coeSort.{succ u5, succ (succ u5)} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) p) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u5} L P _inst_3 p) (FirstOrder.Language.Hom.codRestrict.{u1, u2, u4, u5} L N P _inst_2 _inst_3 p g h) f) (FirstOrder.Language.Hom.codRestrict.{u1, u2, u3, u5} L M P _inst_1 _inst_3 p (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f) (fun (b : M) => h (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f b)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} {P : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u1} L P] (f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u3, u4, u2, u1} L N P _inst_2 _inst_3) (p : FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (h : forall (b : N), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : N) => P) b) (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (FirstOrder.Language.Hom.{u3, u4, u2, u1} L N P _inst_2 _inst_3) N (fun (_x : N) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : N) => P) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u2, u1} L N P _inst_2 _inst_3) g b) p), Eq.{max (succ u5) (succ u1)} (FirstOrder.Language.Hom.{u3, u4, u5, u1} L M (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u3, u4, u1} L P _inst_3 p)) (FirstOrder.Language.Hom.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) x p)) (FirstOrder.Language.Substructure.inducedStructure.{u3, u4, u1} L P _inst_3 p) (FirstOrder.Language.Hom.codRestrict.{u3, u4, u2, u1} L N P _inst_2 _inst_3 p g h) f) (FirstOrder.Language.Hom.codRestrict.{u3, u4, u5, u1} L M P _inst_1 _inst_3 p (FirstOrder.Language.Hom.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 P _inst_3 g f) (fun (b : M) => h (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f b)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.comp_cod_restrict FirstOrder.Language.Hom.comp_codRestrictₓ'. -/
 @[simp]
 theorem comp_codRestrict (f : M →[L] N) (g : N →[L] P) (p : L.Substructure P) (h : ∀ b, g b ∈ p) :
     ((codRestrict p g h).comp f : M →[L] p) = codRestrict p (g.comp f) fun b => h _ :=
   ext fun b => rfl
 #align first_order.language.hom.comp_cod_restrict FirstOrder.Language.Hom.comp_codRestrict
 
-/- warning: first_order.language.hom.subtype_comp_cod_restrict -> FirstOrder.Language.Hom.subtype_comp_codRestrict is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (h : forall (b : M), Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f b) p), Eq.{max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p) N _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u4, u4} L (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) N (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p) _inst_2 (FirstOrder.Language.Substructure.subtype.{u1, u2, u4} L N _inst_2 p)) (FirstOrder.Language.Hom.codRestrict.{u1, u2, u3, u4} L M N _inst_1 _inst_2 p f h)) f
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (h : forall (b : M), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) b) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f b) p), Eq.{max (succ u4) (succ u1)} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (FirstOrder.Language.Hom.comp.{u2, u3, u4, u1, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p) N _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u1, u1} L (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) N (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p) _inst_2 (FirstOrder.Language.Substructure.subtype.{u2, u3, u1} L N _inst_2 p)) (FirstOrder.Language.Hom.codRestrict.{u2, u3, u4, u1} L M N _inst_1 _inst_2 p f h)) f
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.subtype_comp_cod_restrict FirstOrder.Language.Hom.subtype_comp_codRestrictₓ'. -/
 @[simp]
 theorem subtype_comp_codRestrict (f : M →[L] N) (p : L.Substructure N) (h : ∀ b, f b ∈ p) :
     p.Subtype.toHom.comp (codRestrict p f h) = f :=
@@ -1305,42 +921,18 @@ def range (f : M →[L] N) : L.Substructure N :=
 #align first_order.language.hom.range FirstOrder.Language.Hom.range
 -/
 
-/- warning: first_order.language.hom.range_coe -> FirstOrder.Language.Hom.range_coe is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (Set.{u4} N) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)) (Set.range.{u4, succ u3} N M (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (Set.{u1} N) (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)) (Set.range.{u1, succ u4} N M (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f))
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_coe FirstOrder.Language.Hom.range_coeₓ'. -/
 theorem range_coe (f : M →[L] N) : (range f : Set N) = Set.range f :=
   rfl
 #align first_order.language.hom.range_coe FirstOrder.Language.Hom.range_coe
 
-/- warning: first_order.language.hom.mem_range -> FirstOrder.Language.Hom.mem_range is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {x : N}, Iff (Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)) (Exists.{succ u3} M (fun (y : M) => Eq.{succ u4} N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f y) x))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {x : N}, Iff (Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)) (Exists.{succ u4} M (fun (y : M) => Eq.{succ u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) y) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f y) x))
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.mem_range FirstOrder.Language.Hom.mem_rangeₓ'. -/
 @[simp]
 theorem mem_range {f : M →[L] N} {x} : x ∈ range f ↔ ∃ y, f y = x :=
   Iff.rfl
 #align first_order.language.hom.mem_range FirstOrder.Language.Hom.mem_range
 
-/- warning: first_order.language.hom.range_eq_map -> FirstOrder.Language.Hom.range_eq_map is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_eq_map FirstOrder.Language.Hom.range_eq_mapₓ'. -/
 theorem range_eq_map (f : M →[L] N) : f.range = map f ⊤ := by ext; simp
 #align first_order.language.hom.range_eq_map FirstOrder.Language.Hom.range_eq_map
 
-/- warning: first_order.language.hom.mem_range_self -> FirstOrder.Language.Hom.mem_range_self is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (x : M), Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (x : M), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) x) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f x) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.mem_range_self FirstOrder.Language.Hom.mem_range_selfₓ'. -/
 theorem mem_range_self (f : M →[L] N) (x : M) : f x ∈ f.range :=
   ⟨x, rfl⟩
 #align first_order.language.hom.mem_range_self FirstOrder.Language.Hom.mem_range_self
@@ -1352,52 +944,22 @@ theorem range_id : range (id L M) = ⊤ :=
 #align first_order.language.hom.range_id FirstOrder.Language.Hom.range_id
 -/
 
-/- warning: first_order.language.hom.range_comp -> FirstOrder.Language.Hom.range_comp is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3), Eq.{succ u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (FirstOrder.Language.Hom.range.{u1, u2, u3, u5} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f)) (FirstOrder.Language.Substructure.map.{u1, u2, u4, u5} L N P _inst_2 _inst_3 g (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} {P : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u1} L P] (f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u3, u4, u2, u1} L N P _inst_2 _inst_3), Eq.{succ u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (FirstOrder.Language.Hom.range.{u3, u4, u5, u1} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 P _inst_3 g f)) (FirstOrder.Language.Substructure.map.{u3, u4, u2, u1} L N P _inst_2 _inst_3 g (FirstOrder.Language.Hom.range.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_comp FirstOrder.Language.Hom.range_compₓ'. -/
 theorem range_comp (f : M →[L] N) (g : N →[L] P) : range (g.comp f : M →[L] P) = map g (range f) :=
   SetLike.coe_injective (Set.range_comp g f)
 #align first_order.language.hom.range_comp FirstOrder.Language.Hom.range_comp
 
-/- warning: first_order.language.hom.range_comp_le_range -> FirstOrder.Language.Hom.range_comp_le_range is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3), LE.le.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (Preorder.toHasLe.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (SetLike.partialOrder.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)))) (FirstOrder.Language.Hom.range.{u1, u2, u3, u5} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f)) (FirstOrder.Language.Hom.range.{u1, u2, u4, u5} L N P _inst_2 _inst_3 g)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} {P : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u1} L P] (f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u3, u4, u2, u1} L N P _inst_2 _inst_3), LE.le.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u1} L P _inst_3))))) (FirstOrder.Language.Hom.range.{u3, u4, u5, u1} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 P _inst_3 g f)) (FirstOrder.Language.Hom.range.{u3, u4, u2, u1} L N P _inst_2 _inst_3 g)
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_comp_le_range FirstOrder.Language.Hom.range_comp_le_rangeₓ'. -/
 theorem range_comp_le_range (f : M →[L] N) (g : N →[L] P) : range (g.comp f : M →[L] P) ≤ range g :=
   SetLike.coe_mono (Set.range_comp_subset_range f g)
 #align first_order.language.hom.range_comp_le_range FirstOrder.Language.Hom.range_comp_le_range
 
-/- warning: first_order.language.hom.range_eq_top -> FirstOrder.Language.Hom.range_eq_top is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, Iff (Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (Top.top.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u1, u2, u4} L N _inst_2))) (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, Iff (Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) (Top.top.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u2, u3, u1} L N _inst_2))) (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f))
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_eq_top FirstOrder.Language.Hom.range_eq_topₓ'. -/
 theorem range_eq_top {f : M →[L] N} : range f = ⊤ ↔ Function.Surjective f := by
   rw [SetLike.ext'_iff, range_coe, coe_top, Set.range_iff_surjective]
 #align first_order.language.hom.range_eq_top FirstOrder.Language.Hom.range_eq_top
 
-/- warning: first_order.language.hom.range_le_iff_comap -> FirstOrder.Language.Hom.range_le_iff_comap is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p) (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2}, Iff (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p) (Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f p) (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_le_iff_comap FirstOrder.Language.Hom.range_le_iff_comapₓ'. -/
 theorem range_le_iff_comap {f : M →[L] N} {p : L.Substructure N} : range f ≤ p ↔ comap f p = ⊤ := by
   rw [range_eq_map, map_le_iff_le_comap, eq_top_iff]
 #align first_order.language.hom.range_le_iff_comap FirstOrder.Language.Hom.range_le_iff_comap
 
-/- warning: first_order.language.hom.map_le_range -> FirstOrder.Language.Hom.map_le_range is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1}, LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f p) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.map_le_range FirstOrder.Language.Hom.map_le_rangeₓ'. -/
 theorem map_le_range {f : M →[L] N} {p : L.Substructure M} : map f p ≤ range f :=
   SetLike.coe_mono (Set.image_subset_range f p)
 #align first_order.language.hom.map_le_range FirstOrder.Language.Hom.map_le_range
@@ -1414,36 +976,18 @@ def eqLocus (f g : M →[L] N) : Substructure L M
 #align first_order.language.hom.eq_locus FirstOrder.Language.Hom.eqLocus
 -/
 
-/- warning: first_order.language.hom.eq_on_closure -> FirstOrder.Language.Hom.eqOn_closure is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {s : Set.{u3} M}, (Set.EqOn.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) g) s) -> (Set.EqOn.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) g) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {s : Set.{u4} M}, (Set.EqOn.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) g) s) -> (Set.EqOn.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) g) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) s)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.eq_on_closure FirstOrder.Language.Hom.eqOn_closureₓ'. -/
 /-- If two `L.hom`s are equal on a set, then they are equal on its substructure closure. -/
 theorem eqOn_closure {f g : M →[L] N} {s : Set M} (h : Set.EqOn f g s) :
     Set.EqOn f g (closure L s) :=
   show closure L s ≤ f.eqLocus g from closure_le.2 h
 #align first_order.language.hom.eq_on_closure FirstOrder.Language.Hom.eqOn_closure
 
-/- warning: first_order.language.hom.eq_of_eq_on_top -> FirstOrder.Language.Hom.eq_of_eqOn_top is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Set.EqOn.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) g) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1)))) -> (Eq.{max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f g)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Set.EqOn.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) g) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1)))) -> (Eq.{max (succ u4) (succ u1)} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f g)
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.eq_of_eq_on_top FirstOrder.Language.Hom.eq_of_eqOn_topₓ'. -/
 theorem eq_of_eqOn_top {f g : M →[L] N} (h : Set.EqOn f g (⊤ : Substructure L M)) : f = g :=
   ext fun x => h trivial
 #align first_order.language.hom.eq_of_eq_on_top FirstOrder.Language.Hom.eq_of_eqOn_top
 
 variable {s : Set M}
 
-/- warning: first_order.language.hom.eq_of_eq_on_dense -> FirstOrder.Language.Hom.eq_of_eqOn_dense is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {s : Set.{u3} M}, (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1))) -> (forall {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Set.EqOn.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) g) s) -> (Eq.{max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f g))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {s : Set.{u4} M}, (Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) s) (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1))) -> (forall {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Set.EqOn.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) g) s) -> (Eq.{max (succ u4) (succ u1)} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f g))
-Case conversion may be inaccurate. Consider using '#align first_order.language.hom.eq_of_eq_on_dense FirstOrder.Language.Hom.eq_of_eqOn_denseₓ'. -/
 theorem eq_of_eqOn_dense (hs : closure L s = ⊤) {f g : M →[L] N} (h : s.EqOn f g) : f = g :=
   eq_of_eqOn_top <| hs ▸ eqOn_closure h
 #align first_order.language.hom.eq_of_eq_on_dense FirstOrder.Language.Hom.eq_of_eqOn_dense
@@ -1462,9 +1006,6 @@ def domRestrict (f : M ↪[L] N) (p : L.Substructure M) : p ↪[L] N :=
 #align first_order.language.embedding.dom_restrict FirstOrder.Language.Embedding.domRestrict
 -/
 
-/- warning: first_order.language.embedding.dom_restrict_apply -> FirstOrder.Language.Embedding.domRestrict_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.dom_restrict_apply FirstOrder.Language.Embedding.domRestrict_applyₓ'. -/
 @[simp]
 theorem domRestrict_apply (f : M ↪[L] N) (p : L.Substructure M) (x : p) : f.domRestrict p x = f x :=
   rfl
@@ -1487,33 +1028,18 @@ def codRestrict (p : L.Substructure N) (f : M ↪[L] N) (h : ∀ c, f c ∈ p) :
 #align first_order.language.embedding.cod_restrict FirstOrder.Language.Embedding.codRestrict
 -/
 
-/- warning: first_order.language.embedding.cod_restrict_apply -> FirstOrder.Language.Embedding.codRestrict_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.cod_restrict_apply FirstOrder.Language.Embedding.codRestrict_applyₓ'. -/
 @[simp]
 theorem codRestrict_apply (p : L.Substructure N) (f : M ↪[L] N) {h} (x : M) :
     (codRestrict p f h x : N) = f x :=
   rfl
 #align first_order.language.embedding.cod_restrict_apply FirstOrder.Language.Embedding.codRestrict_apply
 
-/- warning: first_order.language.embedding.comp_cod_restrict -> FirstOrder.Language.Embedding.comp_codRestrict is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Embedding.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (p : FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (h : forall (b : N), Membership.Mem.{u5, u5} P (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (SetLike.hasMem.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) (coeFn.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (FirstOrder.Language.Embedding.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u4, u5} L N P _inst_2 _inst_3) => N -> P) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u4, u5} L N P _inst_2 _inst_3) g b) p), Eq.{max (succ u3) (succ u5)} (FirstOrder.Language.Embedding.{u1, u2, u3, u5} L M (coeSort.{succ u5, succ (succ u5)} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u5} L P _inst_3 p)) (FirstOrder.Language.Embedding.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 (coeSort.{succ u5, succ (succ u5)} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) p) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u5} L P _inst_3 p) (FirstOrder.Language.Embedding.codRestrict.{u1, u2, u4, u5} L N P _inst_2 _inst_3 p g h) f) (FirstOrder.Language.Embedding.codRestrict.{u1, u2, u3, u5} L M P _inst_1 _inst_3 p (FirstOrder.Language.Embedding.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f) (fun (b : M) => h (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f b)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} {P : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u1} L P] (f : FirstOrder.Language.Embedding.{u3, u4, u5, u2} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Embedding.{u3, u4, u2, u1} L N P _inst_2 _inst_3) (p : FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (h : forall (b : N), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : N) => P) b) (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (FirstOrder.Language.Embedding.{u3, u4, u2, u1} L N P _inst_2 _inst_3) N (fun (_x : N) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : N) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (FirstOrder.Language.Embedding.{u3, u4, u2, u1} L N P _inst_2 _inst_3) N P (FirstOrder.Language.Embedding.embeddingLike.{u3, u4, u2, u1} L N P _inst_2 _inst_3)) g b) p), Eq.{max (succ u5) (succ u1)} (FirstOrder.Language.Embedding.{u3, u4, u5, u1} L M (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u3, u4, u1} L P _inst_3 p)) (FirstOrder.Language.Embedding.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) x p)) (FirstOrder.Language.Substructure.inducedStructure.{u3, u4, u1} L P _inst_3 p) (FirstOrder.Language.Embedding.codRestrict.{u3, u4, u2, u1} L N P _inst_2 _inst_3 p g h) f) (FirstOrder.Language.Embedding.codRestrict.{u3, u4, u5, u1} L M P _inst_1 _inst_3 p (FirstOrder.Language.Embedding.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 P _inst_3 g f) (fun (b : M) => h (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Embedding.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Embedding.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2)) f b)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.comp_cod_restrict FirstOrder.Language.Embedding.comp_codRestrictₓ'. -/
 @[simp]
 theorem comp_codRestrict (f : M ↪[L] N) (g : N ↪[L] P) (p : L.Substructure P) (h : ∀ b, g b ∈ p) :
     ((codRestrict p g h).comp f : M ↪[L] p) = codRestrict p (g.comp f) fun b => h _ :=
   ext fun b => rfl
 #align first_order.language.embedding.comp_cod_restrict FirstOrder.Language.Embedding.comp_codRestrict
 
-/- warning: first_order.language.embedding.subtype_comp_cod_restrict -> FirstOrder.Language.Embedding.subtype_comp_codRestrict is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (h : forall (b : M), Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f b) p), Eq.{max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (FirstOrder.Language.Embedding.comp.{u1, u2, u3, u4, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p) N _inst_2 (FirstOrder.Language.Substructure.subtype.{u1, u2, u4} L N _inst_2 p) (FirstOrder.Language.Embedding.codRestrict.{u1, u2, u3, u4} L M N _inst_1 _inst_2 p f h)) f
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (h : forall (b : M), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) b) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f b) p), Eq.{max (succ u4) (succ u1)} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (FirstOrder.Language.Embedding.comp.{u2, u3, u4, u1, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p) N _inst_2 (FirstOrder.Language.Substructure.subtype.{u2, u3, u1} L N _inst_2 p) (FirstOrder.Language.Embedding.codRestrict.{u2, u3, u4, u1} L M N _inst_1 _inst_2 p f h)) f
-Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.subtype_comp_cod_restrict FirstOrder.Language.Embedding.subtype_comp_codRestrictₓ'. -/
 @[simp]
 theorem subtype_comp_codRestrict (f : M ↪[L] N) (p : L.Substructure N) (h : ∀ b, f b ∈ p) :
     p.Subtype.comp (codRestrict p f h) = f :=
@@ -1537,9 +1063,6 @@ noncomputable def substructureEquivMap (f : M ↪[L] N) (s : L.Substructure M) :
 #align first_order.language.embedding.substructure_equiv_map FirstOrder.Language.Embedding.substructureEquivMap
 -/
 
-/- warning: first_order.language.embedding.substructure_equiv_map_apply -> FirstOrder.Language.Embedding.substructureEquivMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.substructure_equiv_map_apply FirstOrder.Language.Embedding.substructureEquivMap_applyₓ'. -/
 @[simp]
 theorem substructureEquivMap_apply (f : M ↪[L] N) (p : L.Substructure M) (x : p) :
     (f.substructureEquivMap p x : N) = f x :=
@@ -1558,9 +1081,6 @@ noncomputable def equivRange (f : M ↪[L] N) : M ≃[L] f.toHom.range
 #align first_order.language.embedding.equiv_range FirstOrder.Language.Embedding.equivRange
 -/
 
-/- warning: first_order.language.embedding.equiv_range_apply -> FirstOrder.Language.Embedding.equivRange_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.equiv_range_apply FirstOrder.Language.Embedding.equivRange_applyₓ'. -/
 @[simp]
 theorem equivRange_apply (f : M ↪[L] N) (x : M) : (f.equivRange x : N) = f x :=
   rfl
@@ -1570,12 +1090,6 @@ end Embedding
 
 namespace Equiv
 
-/- warning: first_order.language.equiv.to_hom_range -> FirstOrder.Language.Equiv.toHom_range is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Equiv.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Equiv.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)) (Top.top.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u1, u2, u4} L N _inst_2))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Equiv.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Equiv.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)) (Top.top.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u2, u3, u1} L N _inst_2))
-Case conversion may be inaccurate. Consider using '#align first_order.language.equiv.to_hom_range FirstOrder.Language.Equiv.toHom_rangeₓ'. -/
 theorem toHom_range (f : M ≃[L] N) : f.toHom.range = ⊤ :=
   by
   ext n
@@ -1587,20 +1101,11 @@ end Equiv
 
 namespace Substructure
 
-/- warning: first_order.language.substructure.inclusion -> FirstOrder.Language.Substructure.inclusion is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T) -> (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S T) -> (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.inclusion FirstOrder.Language.Substructure.inclusionₓ'. -/
 /-- The embedding associated to an inclusion of substructures. -/
 def inclusion {S T : L.Substructure M} (h : S ≤ T) : S ↪[L] T :=
   S.Subtype.codRestrict _ fun x => h x.2
 #align first_order.language.substructure.inclusion FirstOrder.Language.Substructure.inclusion
 
-/- warning: first_order.language.substructure.coe_inclusion -> FirstOrder.Language.Substructure.coe_inclusion is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.coe_inclusion FirstOrder.Language.Substructure.coe_inclusionₓ'. -/
 @[simp]
 theorem coe_inclusion {S T : L.Substructure M} (h : S ≤ T) :
     (inclusion h : S → T) = Set.inclusion h :=

6cf59007

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -1219,9 +1219,7 @@ theorem coe_withConstants : (S.withConstants h : Set M) = ↑S :=
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.reduct_with_constants FirstOrder.Language.Substructure.reduct_withConstantsₓ'. -/
 @[simp]
 theorem reduct_withConstants : (L.lhomWithConstants A).substructureReduct (S.withConstants h) = S :=
-  by
-  ext
-  simp
+  by ext; simp
 #align first_order.language.substructure.reduct_with_constants FirstOrder.Language.Substructure.reduct_withConstants
 
 #print FirstOrder.Language.Substructure.subset_closure_withConstants /-
@@ -1334,10 +1332,7 @@ lean 3 declaration is
 but is expected to have type
   forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1)))
 Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_eq_map FirstOrder.Language.Hom.range_eq_mapₓ'. -/
-theorem range_eq_map (f : M →[L] N) : f.range = map f ⊤ :=
-  by
-  ext
-  simp
+theorem range_eq_map (f : M →[L] N) : f.range = map f ⊤ := by ext; simp
 #align first_order.language.hom.range_eq_map FirstOrder.Language.Hom.range_eq_map
 
 /- warning: first_order.language.hom.mem_range_self -> FirstOrder.Language.Hom.mem_range_self is a dubious translation:
@@ -1414,10 +1409,7 @@ def eqLocus (f g : M →[L] N) : Substructure L M
   carrier := { x : M | f x = g x }
   fun_mem n fn x hx :=
     by
-    have h : f ∘ x = g ∘ x := by
-      ext
-      repeat' rw [Function.comp_apply]
-      apply hx
+    have h : f ∘ x = g ∘ x := by ext; repeat' rw [Function.comp_apply]; apply hx
     simp [h]
 #align first_order.language.hom.eq_locus FirstOrder.Language.Hom.eqLocus
 -/

6cf59007

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -372,10 +372,7 @@ theorem closure_le : closure L s ≤ S ↔ s ⊆ S :=
 #align first_order.language.substructure.closure_le FirstOrder.Language.Substructure.closure_le
 
 /- warning: first_order.language.substructure.closure_mono -> FirstOrder.Language.Substructure.closure_mono is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {{s : Set.{u3} M}} {{t : Set.{u3} M}}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s t) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) t))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {{s : Set.{u3} M}} {{t : Set.{u3} M}}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) s t) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) t))
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_mono FirstOrder.Language.Substructure.closure_monoₓ'. -/
 /-- Substructure closure of a set is monotone in its argument: if `s ⊆ t`,
 then `closure L s ≤ closure L t`. -/
@@ -384,10 +381,7 @@ theorem closure_mono ⦃s t : Set M⦄ (h : s ⊆ t) : closure L s ≤ closure L
 #align first_order.language.substructure.closure_mono FirstOrder.Language.Substructure.closure_mono
 
 /- warning: first_order.language.substructure.closure_eq_of_le -> FirstOrder.Language.Substructure.closure_eq_of_le is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)) -> (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) s (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S)) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)) -> (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S)
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_eq_of_le FirstOrder.Language.Substructure.closure_eq_of_leₓ'. -/
 theorem closure_eq_of_le (h₁ : s ⊆ S) (h₂ : S ≤ closure L s) : closure L s = S :=
   (closure L).eq_of_le h₁ h₂
@@ -531,20 +525,14 @@ theorem closure_univ : closure L (univ : Set M) = ⊤ :=
 -/
 
 /- warning: first_order.language.substructure.closure_union -> FirstOrder.Language.Substructure.closure_union is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] (s : Set.{u3} M) (t : Set.{u3} M), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.hasUnion.{u3} M) s t)) (Sup.sup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SemilatticeSup.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Lattice.toSemilatticeSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) t))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] (s : Set.{u3} M) (t : Set.{u3} M), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.instUnionSet.{u3} M) s t)) (Sup.sup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SemilatticeSup.toSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Lattice.toSemilatticeSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) t))
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_union FirstOrder.Language.Substructure.closure_unionₓ'. -/
 theorem closure_union (s t : Set M) : closure L (s ∪ t) = closure L s ⊔ closure L t :=
   (Substructure.gi L M).gc.l_sup
 #align first_order.language.substructure.closure_union FirstOrder.Language.Substructure.closure_union
 
 /- warning: first_order.language.substructure.closure_Union -> FirstOrder.Language.Substructure.closure_unionᵢ is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} (s : ι -> (Set.{u3} M)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Set.iUnion.{u3, u4} M ι (fun (i : ι) => s i))) (iSup.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι (fun (i : ι) => coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (s i)))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} (s : ι -> (Set.{u4} M)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) (Set.iUnion.{u4, u1} M ι (fun (i : ι) => s i))) (iSup.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))) ι (fun (i : ι) => LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) (s i)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_Union FirstOrder.Language.Substructure.closure_unionᵢₓ'. -/
 theorem closure_unionᵢ {ι} (s : ι → Set M) : closure L (⋃ i, s i) = ⨆ i, closure L (s i) :=
   (Substructure.gi L M).gc.l_iSup
@@ -846,10 +834,7 @@ theorem map_id (S : L.Substructure M) : S.map (Hom.id L M) = S :=
 -/
 
 /- warning: first_order.language.substructure.map_closure -> FirstOrder.Language.Substructure.map_closure is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (s : Set.{u3} M), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)) (coeFn.{succ u4, succ u4} (LowerAdjoint.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) (fun (_x : LowerAdjoint.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) => (Set.{u4} N) -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)) (LowerAdjoint.hasCoeToFun.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u4} L N _inst_2) (Set.image.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) s))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (s : Set.{u4} M), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) s)) (LowerAdjoint.toFun.{u1, u1} (Set.{u1} N) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (Set.{u1} N) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} N) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} N) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} N) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} N) (Set.instCompleteBooleanAlgebraSet.{u1} N))))))) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FirstOrder.Language.Substructure.closure.{u2, u3, u1} L N _inst_2) (Set.image.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) s))
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_closure FirstOrder.Language.Substructure.map_closureₓ'. -/
 theorem map_closure (f : M →[L] N) (s : Set M) : (closure L s).map f = closure L (f '' s) :=
   Eq.symm <|
@@ -858,10 +843,7 @@ theorem map_closure (f : M →[L] N) (s : Set M) : (closure L s).map f = closure
 #align first_order.language.substructure.map_closure FirstOrder.Language.Substructure.map_closure
 
 /- warning: first_order.language.substructure.closure_image -> FirstOrder.Language.Substructure.closure_image is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {s : Set.{u3} M} (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (coeFn.{succ u4, succ u4} (LowerAdjoint.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) (fun (_x : LowerAdjoint.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) => (Set.{u4} N) -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)) (LowerAdjoint.hasCoeToFun.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u4} L N _inst_2) (Set.image.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) s)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {s : Set.{u4} M} (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (LowerAdjoint.toFun.{u1, u1} (Set.{u1} N) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (Set.{u1} N) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} N) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} N) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} N) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} N) (Set.instCompleteBooleanAlgebraSet.{u1} N))))))) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FirstOrder.Language.Substructure.closure.{u2, u3, u1} L N _inst_2) (Set.image.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) s)) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) s))
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_image FirstOrder.Language.Substructure.closure_imageₓ'. -/
 @[simp]
 theorem closure_image (f : M →[L] N) : closure L (f '' s) = map f (closure L s) :=
@@ -1182,10 +1164,7 @@ def substructureReduct : L'.Substructure M ↪o L.Substructure M
 #align first_order.language.Lhom.substructure_reduct FirstOrder.Language.LHom.substructureReduct
 
 /- warning: first_order.language.Lhom.mem_substructure_reduct -> FirstOrder.Language.LHom.mem_substructureReduct is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4] {x : M} {S : FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4}, Iff (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, u4, u5} L M _inst_1 L' _inst_4 φ _inst_5) S)) (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)) x S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] {L' : FirstOrder.Language.{u2, u1}} [_inst_4 : FirstOrder.Language.Structure.{u2, u1, u5} L' M] (φ : FirstOrder.Language.LHom.{u3, u4, u2, u1} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u3, u4, u2, u1, u5} L L' φ M _inst_1 _inst_4] {x : M} {S : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4}, Iff (Membership.mem.{u5, u5} M ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) (SetLike.instMembership.{u5, u5} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) M (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u5} L M _inst_1)) x (FunLike.coe.{succ u5, succ u5, succ u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (fun (_x : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) _x) (RelHomClass.toFunLike.{u5, u5, u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (FirstOrder.Language.LHom.substructureReduct.{u3, u4, u5, u2, u1} L M _inst_1 L' _inst_4 φ _inst_5) S)) (Membership.mem.{u5, u5} M (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (SetLike.instMembership.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u2, u1, u5} L' M _inst_4)) x S)
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.mem_substructure_reduct FirstOrder.Language.LHom.mem_substructureReductₓ'. -/
 @[simp]
 theorem mem_substructureReduct {x : M} {S : L'.Substructure M} :
@@ -1194,10 +1173,7 @@ theorem mem_substructureReduct {x : M} {S : L'.Substructure M} :
 #align first_order.language.Lhom.mem_substructure_reduct FirstOrder.Language.LHom.mem_substructureReduct
 
 /- warning: first_order.language.Lhom.coe_substructure_reduct -> FirstOrder.Language.LHom.coe_substructureReduct is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4] {S : FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4}, Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, u4, u5} L M _inst_1 L' _inst_4 φ _inst_5) S)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) S)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] {L' : FirstOrder.Language.{u2, u1}} [_inst_4 : FirstOrder.Language.Structure.{u2, u1, u5} L' M] (φ : FirstOrder.Language.LHom.{u3, u4, u2, u1} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u3, u4, u2, u1, u5} L L' φ M _inst_1 _inst_4] {S : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4}, Eq.{succ u5} (Set.{u5} M) (SetLike.coe.{u5, u5} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) M (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u5} L M _inst_1) (FunLike.coe.{succ u5, succ u5, succ u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (fun (_x : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) _x) (RelHomClass.toFunLike.{u5, u5, u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (FirstOrder.Language.LHom.substructureReduct.{u3, u4, u5, u2, u1} L M _inst_1 L' _inst_4 φ _inst_5) S)) (SetLike.coe.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u2, u1, u5} L' M _inst_4) S)
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.coe_substructure_reduct FirstOrder.Language.LHom.coe_substructureReductₓ'. -/
 @[simp]
 theorem coe_substructureReduct {S : L'.Substructure M} : (φ.substructureReduct S : Set M) = ↑S :=
@@ -1239,10 +1215,7 @@ theorem coe_withConstants : (S.withConstants h : Set M) = ↑S :=
 -/
 
 /- warning: first_order.language.substructure.reduct_with_constants -> FirstOrder.Language.Substructure.reduct_withConstants is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {A : Set.{u3} M} (h : HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) A ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, max u1 u3, u2} L M _inst_1 (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)) (FirstOrder.Language.lhomWithConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) (FirstOrder.Language.withConstants_expansion.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) S
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {A : Set.{u3} M} (h : HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) A (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S)), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (fun (_x : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) => LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) => LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, max u1 u3, u2} L M _inst_1 (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A)) (FirstOrder.Language.lhomWithConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) (FirstOrder.Language.withConstants_expansion.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) S
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.reduct_with_constants FirstOrder.Language.Substructure.reduct_withConstantsₓ'. -/
 @[simp]
 theorem reduct_withConstants : (L.lhomWithConstants A).substructureReduct (S.withConstants h) = S :=
@@ -1262,10 +1235,7 @@ theorem subset_closure_withConstants : A ⊆ closure (L[[A]]) s :=
 -/
 
 /- warning: first_order.language.substructure.closure_with_constants_eq -> FirstOrder.Language.Substructure.closure_withConstants_eq is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {A : Set.{u3} M} {s : Set.{u3} M}, Eq.{succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))))))) (FirstOrder.Language.Substructure.closure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) s) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.hasUnion.{u3} M) A s)) A (HasSubset.Subset.trans.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) (Set.hasSubset.Subset.isTrans.{u3} M) A (Union.union.{u3} (Set.{u3} M) (Set.hasUnion.{u3} M) A s) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.hasUnion.{u3} M) A s))) (Set.subset_union_left.{u3} M A s) (FirstOrder.Language.Substructure.subset_closure.{u1, u2, u3} L M _inst_1 (Union.union.{u3} (Set.{u3} M) (Set.hasUnion.{u3} M) A s))))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {A : Set.{u3} M} {s : Set.{u3} M}, Eq.{succ u3} (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A)))))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A)))) (FirstOrder.Language.Substructure.closure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) s) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.instUnionSet.{u3} M) A s)) A (HasSubset.Subset.trans.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) (Set.instIsTransSetSubsetInstHasSubsetSet.{u3} M) A (Union.union.{u3} (Set.{u3} M) (Set.instUnionSet.{u3} M) A s) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.instUnionSet.{u3} M) A s))) (Set.subset_union_left.{u3} M A s) (FirstOrder.Language.Substructure.subset_closure.{u1, u2, u3} L M _inst_1 (Union.union.{u3} (Set.{u3} M) (Set.instUnionSet.{u3} M) A s))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_with_constants_eq FirstOrder.Language.Substructure.closure_withConstants_eqₓ'. -/
 theorem closure_withConstants_eq :
     closure (L[[A]]) s =
@@ -1501,10 +1471,7 @@ def domRestrict (f : M ↪[L] N) (p : L.Substructure M) : p ↪[L] N :=
 -/
 
 /- warning: first_order.language.embedding.dom_restrict_apply -> FirstOrder.Language.Embedding.domRestrict_apply is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x : coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p), Eq.{succ u4} N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) N (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) N (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) _inst_2) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) N (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) _inst_2) (FirstOrder.Language.Embedding.domRestrict.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (coeSubtype.{succ u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x p))))) x))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (x : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)), Eq.{succ u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) => N) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) N (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) _inst_2) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (fun (_x : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) N (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) _inst_2) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) N (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) _inst_2)) (FirstOrder.Language.Embedding.domRestrict.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f p) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f (Subtype.val.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Set.{u4} M) (Set.instMembershipSet.{u4} M) x (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) p)) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.dom_restrict_apply FirstOrder.Language.Embedding.domRestrict_applyₓ'. -/
 @[simp]
 theorem domRestrict_apply (f : M ↪[L] N) (p : L.Substructure M) (x : p) : f.domRestrict p x = f x :=
@@ -1529,10 +1496,7 @@ def codRestrict (p : L.Substructure N) (f : M ↪[L] N) (h : ∀ c, f c ∈ p) :
 -/
 
 /- warning: first_order.language.embedding.cod_restrict_apply -> FirstOrder.Language.Embedding.codRestrict_apply is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (p : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) {h : forall (c : M), Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f c) p} (x : M), Eq.{succ u4} N ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) N (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) N (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) N (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) N (coeSubtype.{succ u4} N (fun (x : N) => Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) x p))))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p)) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p)) => M -> (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p)) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p)) (FirstOrder.Language.Embedding.codRestrict.{u1, u2, u3, u4} L M N _inst_1 _inst_2 p f h) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (p : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (f : FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) {h : forall (c : M), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) c) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f c) p} (x : M), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2) p)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p)) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p)) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p))) (FirstOrder.Language.Embedding.codRestrict.{u2, u3, u4, u1} L M N _inst_1 _inst_2 p f h) x)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.cod_restrict_apply FirstOrder.Language.Embedding.codRestrict_applyₓ'. -/
 @[simp]
 theorem codRestrict_apply (p : L.Substructure N) (f : M ↪[L] N) {h} (x : M) :
@@ -1582,10 +1546,7 @@ noncomputable def substructureEquivMap (f : M ↪[L] N) (s : L.Substructure M) :
 -/
 
 /- warning: first_order.language.embedding.substructure_equiv_map_apply -> FirstOrder.Language.Embedding.substructureEquivMap_apply is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x : coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p), Eq.{succ u4} N ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) N (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) N (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) N (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) N (coeSubtype.{succ u4} N (fun (x : N) => Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)))))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Equiv.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p))) (fun (_x : FirstOrder.Language.Equiv.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p))) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) -> (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Equiv.hasCoeToFun.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Embedding.substructureEquivMap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (coeSubtype.{succ u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x p))))) x))
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (x : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (fun (_x : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.8209 : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (EquivLike.toEmbeddingLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Equiv.instEquivLikeEquiv.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))))) (FirstOrder.Language.Embedding.substructureEquivMap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f p) x)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f (Subtype.val.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Set.{u4} M) (Set.instMembershipSet.{u4} M) x (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) p)) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.substructure_equiv_map_apply FirstOrder.Language.Embedding.substructureEquivMap_applyₓ'. -/
 @[simp]
 theorem substructureEquivMap_apply (f : M ↪[L] N) (p : L.Substructure M) (x : p) :
@@ -1606,10 +1567,7 @@ noncomputable def equivRange (f : M ↪[L] N) : M ≃[L] f.toHom.range
 -/
 
 /- warning: first_order.language.embedding.equiv_range_apply -> FirstOrder.Language.Embedding.equivRange_apply is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (x : M), Eq.{succ u4} N ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) N (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) N (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) N (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) N (coeSubtype.{succ u4} N (fun (x : N) => Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))))))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Equiv.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)))) (fun (_x : FirstOrder.Language.Equiv.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)))) => M -> (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)))) (FirstOrder.Language.Equiv.hasCoeToFun.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)))) (FirstOrder.Language.Embedding.equivRange.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (x : M), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.8209 : M) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) (EquivLike.toEmbeddingLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) (FirstOrder.Language.Equiv.instEquivLikeEquiv.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))))) (FirstOrder.Language.Embedding.equivRange.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) x)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.equiv_range_apply FirstOrder.Language.Embedding.equivRange_applyₓ'. -/
 @[simp]
 theorem equivRange_apply (f : M ↪[L] N) (x : M) : (f.equivRange x : N) = f x :=
@@ -1649,10 +1607,7 @@ def inclusion {S T : L.Substructure M} (h : S ≤ T) : S ↪[L] T :=
 #align first_order.language.substructure.inclusion FirstOrder.Language.Substructure.inclusion
 
 /- warning: first_order.language.substructure.coe_inclusion -> FirstOrder.Language.Substructure.coe_inclusion is a dubious translation:
-lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} (h : LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T), Eq.{succ u3} ((fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) -> (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T)) (FirstOrder.Language.Substructure.inclusion.{u1, u2, u3} L M _inst_1 S T h)) (coeFn.{succ u3, succ u3} (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) -> (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T)) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (FirstOrder.Language.Substructure.inclusion.{u1, u2, u3} L M _inst_1 S T h)) (Set.inclusion.{u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) x ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)) (fun (x : M) => Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) x ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) T)) h)
-but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} (h : LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S T), Eq.{succ u3} (forall (a : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)), (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) a) (FunLike.coe.{succ u3, succ u3, succ u3} (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (fun (_x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) _x) (EmbeddingLike.toFunLike.{succ u3, succ u3, succ u3} (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Embedding.embeddingLike.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T))) (FirstOrder.Language.Substructure.inclusion.{u1, u2, u3} L M _inst_1 S T h)) (Set.inclusion.{u3} M (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) T) h)
+<too large>
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.coe_inclusion FirstOrder.Language.Substructure.coe_inclusionₓ'. -/
 @[simp]
 theorem coe_inclusion {S T : L.Substructure M} (h : S ≤ T) :

6cf59007

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -1185,7 +1185,7 @@ def substructureReduct : L'.Substructure M ↪o L.Substructure M
 lean 3 declaration is
   forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4] {x : M} {S : FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4}, Iff (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, u4, u5} L M _inst_1 L' _inst_4 φ _inst_5) S)) (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)) x S)
 but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] {L' : FirstOrder.Language.{u2, u1}} [_inst_4 : FirstOrder.Language.Structure.{u2, u1, u5} L' M] (φ : FirstOrder.Language.LHom.{u3, u4, u2, u1} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u3, u4, u2, u1, u5} L L' φ M _inst_1 _inst_4] {x : M} {S : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4}, Iff (Membership.mem.{u5, u5} M ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) (SetLike.instMembership.{u5, u5} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) M (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u5} L M _inst_1)) x (FunLike.coe.{succ u5, succ u5, succ u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (fun (_x : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) _x) (RelHomClass.toFunLike.{u5, u5, u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (FirstOrder.Language.LHom.substructureReduct.{u3, u4, u5, u2, u1} L M _inst_1 L' _inst_4 φ _inst_5) S)) (Membership.mem.{u5, u5} M (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (SetLike.instMembership.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u2, u1, u5} L' M _inst_4)) x S)
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] {L' : FirstOrder.Language.{u2, u1}} [_inst_4 : FirstOrder.Language.Structure.{u2, u1, u5} L' M] (φ : FirstOrder.Language.LHom.{u3, u4, u2, u1} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u3, u4, u2, u1, u5} L L' φ M _inst_1 _inst_4] {x : M} {S : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4}, Iff (Membership.mem.{u5, u5} M ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) (SetLike.instMembership.{u5, u5} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) M (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u5} L M _inst_1)) x (FunLike.coe.{succ u5, succ u5, succ u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (fun (_x : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) _x) (RelHomClass.toFunLike.{u5, u5, u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (FirstOrder.Language.LHom.substructureReduct.{u3, u4, u5, u2, u1} L M _inst_1 L' _inst_4 φ _inst_5) S)) (Membership.mem.{u5, u5} M (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (SetLike.instMembership.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u2, u1, u5} L' M _inst_4)) x S)
 Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.mem_substructure_reduct FirstOrder.Language.LHom.mem_substructureReductₓ'. -/
 @[simp]
 theorem mem_substructureReduct {x : M} {S : L'.Substructure M} :
@@ -1197,7 +1197,7 @@ theorem mem_substructureReduct {x : M} {S : L'.Substructure M} :
 lean 3 declaration is
   forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4] {S : FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4}, Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, u4, u5} L M _inst_1 L' _inst_4 φ _inst_5) S)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) S)
 but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] {L' : FirstOrder.Language.{u2, u1}} [_inst_4 : FirstOrder.Language.Structure.{u2, u1, u5} L' M] (φ : FirstOrder.Language.LHom.{u3, u4, u2, u1} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u3, u4, u2, u1, u5} L L' φ M _inst_1 _inst_4] {S : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4}, Eq.{succ u5} (Set.{u5} M) (SetLike.coe.{u5, u5} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) M (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u5} L M _inst_1) (FunLike.coe.{succ u5, succ u5, succ u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (fun (_x : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) _x) (RelHomClass.toFunLike.{u5, u5, u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (FirstOrder.Language.LHom.substructureReduct.{u3, u4, u5, u2, u1} L M _inst_1 L' _inst_4 φ _inst_5) S)) (SetLike.coe.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u2, u1, u5} L' M _inst_4) S)
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] {L' : FirstOrder.Language.{u2, u1}} [_inst_4 : FirstOrder.Language.Structure.{u2, u1, u5} L' M] (φ : FirstOrder.Language.LHom.{u3, u4, u2, u1} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u3, u4, u2, u1, u5} L L' φ M _inst_1 _inst_4] {S : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4}, Eq.{succ u5} (Set.{u5} M) (SetLike.coe.{u5, u5} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) M (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u5} L M _inst_1) (FunLike.coe.{succ u5, succ u5, succ u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (fun (_x : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) _x) (RelHomClass.toFunLike.{u5, u5, u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (FirstOrder.Language.LHom.substructureReduct.{u3, u4, u5, u2, u1} L M _inst_1 L' _inst_4 φ _inst_5) S)) (SetLike.coe.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u2, u1, u5} L' M _inst_4) S)
 Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.coe_substructure_reduct FirstOrder.Language.LHom.coe_substructureReductₓ'. -/
 @[simp]
 theorem coe_substructureReduct {S : L'.Substructure M} : (φ.substructureReduct S : Set M) = ↑S :=
@@ -1242,7 +1242,7 @@ theorem coe_withConstants : (S.withConstants h : Set M) = ↑S :=
 lean 3 declaration is
   forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {A : Set.{u3} M} (h : HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) A ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, max u1 u3, u2} L M _inst_1 (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)) (FirstOrder.Language.lhomWithConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) (FirstOrder.Language.withConstants_expansion.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) S
 but is expected to have type
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {A : Set.{u3} M} (h : HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) A (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S)), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (fun (_x : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) => LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) => LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, max u1 u3, u2} L M _inst_1 (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A)) (FirstOrder.Language.lhomWithConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) (FirstOrder.Language.withConstants_expansion.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) S
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {A : Set.{u3} M} (h : HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) A (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S)), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (fun (_x : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) => LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) => LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, max u1 u3, u2} L M _inst_1 (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A)) (FirstOrder.Language.lhomWithConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) (FirstOrder.Language.withConstants_expansion.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) S
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.reduct_with_constants FirstOrder.Language.Substructure.reduct_withConstantsₓ'. -/
 @[simp]
 theorem reduct_withConstants : (L.lhomWithConstants A).substructureReduct (S.withConstants h) = S :=

6cf59007

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -361,7 +361,7 @@ open Set
 
 /- warning: first_order.language.substructure.closure_le -> FirstOrder.Language.Substructure.closure_le is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, Iff (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S) (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, Iff (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S) (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S))
 but is expected to have type
   forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, Iff (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S) (HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) s (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S))
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_le FirstOrder.Language.Substructure.closure_leₓ'. -/
@@ -373,7 +373,7 @@ theorem closure_le : closure L s ≤ S ↔ s ⊆ S :=
 
 /- warning: first_order.language.substructure.closure_mono -> FirstOrder.Language.Substructure.closure_mono is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {{s : Set.{u3} M}} {{t : Set.{u3} M}}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s t) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) t))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {{s : Set.{u3} M}} {{t : Set.{u3} M}}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s t) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) t))
 but is expected to have type
   forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {{s : Set.{u3} M}} {{t : Set.{u3} M}}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) s t) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_mono FirstOrder.Language.Substructure.closure_monoₓ'. -/
@@ -385,7 +385,7 @@ theorem closure_mono ⦃s t : Set M⦄ (h : s ⊆ t) : closure L s ≤ closure L
 
 /- warning: first_order.language.substructure.closure_eq_of_le -> FirstOrder.Language.Substructure.closure_eq_of_le is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)) -> (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S)
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)) -> (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S)
 but is expected to have type
   forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) s (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S)) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)) -> (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S)
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_eq_of_le FirstOrder.Language.Substructure.closure_eq_of_leₓ'. -/
@@ -671,7 +671,7 @@ theorem map_map (g : N →[L] P) (f : M →[L] N) : (S.map f).map g = S.map (g.c
 
 /- warning: first_order.language.substructure.map_le_iff_le_comap -> FirstOrder.Language.Substructure.map_le_iff_le_comap is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
 but is expected to have type
   forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2}, Iff (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) T) (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_le_iff_le_comap FirstOrder.Language.Substructure.map_le_iff_le_comapₓ'. -/
@@ -692,7 +692,7 @@ theorem gc_map_comap (f : M →[L] N) : GaloisConnection (map f) (comap f) := fu
 
 /- warning: first_order.language.substructure.map_le_of_le_comap -> FirstOrder.Language.Substructure.map_le_of_le_comap is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) -> (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T)
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) -> (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T)
 but is expected to have type
   forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T)) -> (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) T)
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_le_of_le_comap FirstOrder.Language.Substructure.map_le_of_le_comapₓ'. -/
@@ -702,7 +702,7 @@ theorem map_le_of_le_comap {T : L.Substructure N} {f : M →[L] N} : S ≤ T.com
 
 /- warning: first_order.language.substructure.le_comap_of_map_le -> FirstOrder.Language.Substructure.le_comap_of_map_le is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
 but is expected to have type
   forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) T) -> (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.le_comap_of_map_le FirstOrder.Language.Substructure.le_comap_of_map_leₓ'. -/
@@ -712,7 +712,7 @@ theorem le_comap_of_map_le {T : L.Substructure N} {f : M →[L] N} : S.map f ≤
 
 /- warning: first_order.language.substructure.le_comap_map -> FirstOrder.Language.Substructure.le_comap_map is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S))
 but is expected to have type
   forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S))
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.le_comap_map FirstOrder.Language.Substructure.le_comap_mapₓ'. -/
@@ -722,7 +722,7 @@ theorem le_comap_map {f : M →[L] N} : S ≤ (S.map f).comap f :=
 
 /- warning: first_order.language.substructure.map_comap_le -> FirstOrder.Language.Substructure.map_comap_le is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) S
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) S
 but is expected to have type
   forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)) S
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_comap_le FirstOrder.Language.Substructure.map_comap_leₓ'. -/
@@ -959,7 +959,7 @@ theorem comap_iSup_map_of_injective (S : ι → L.Substructure M) :
 
 /- warning: first_order.language.substructure.map_le_map_iff_of_injective -> FirstOrder.Language.Substructure.map_le_map_iff_of_injective is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T))
 but is expected to have type
   forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {T : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1}, Iff (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T)) (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S T))
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_le_map_iff_of_injective FirstOrder.Language.Substructure.map_le_map_iff_of_injectiveₓ'. -/
@@ -1074,7 +1074,7 @@ theorem map_iSup_comap_of_surjective (S : ι → L.Substructure N) :
 
 /- warning: first_order.language.substructure.comap_le_comap_iff_of_surjective -> FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjective is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) S T))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) S T))
 but is expected to have type
   forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T)) (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) S T))
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_le_comap_iff_of_surjective FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjectiveₓ'. -/
@@ -1161,7 +1161,7 @@ include φ
 
 /- warning: first_order.language.Lhom.substructure_reduct -> FirstOrder.Language.LHom.substructureReduct is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4], OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4], OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))
 but is expected to have type
   forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4], OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u4, u5, u3} L' M _inst_4))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.substructure_reduct FirstOrder.Language.LHom.substructureReductₓ'. -/
@@ -1183,7 +1183,7 @@ def substructureReduct : L'.Substructure M ↪o L.Substructure M
 
 /- warning: first_order.language.Lhom.mem_substructure_reduct -> FirstOrder.Language.LHom.mem_substructureReduct is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4] {x : M} {S : FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4}, Iff (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, u4, u5} L M _inst_1 L' _inst_4 φ _inst_5) S)) (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)) x S)
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4] {x : M} {S : FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4}, Iff (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, u4, u5} L M _inst_1 L' _inst_4 φ _inst_5) S)) (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)) x S)
 but is expected to have type
   forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] {L' : FirstOrder.Language.{u2, u1}} [_inst_4 : FirstOrder.Language.Structure.{u2, u1, u5} L' M] (φ : FirstOrder.Language.LHom.{u3, u4, u2, u1} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u3, u4, u2, u1, u5} L L' φ M _inst_1 _inst_4] {x : M} {S : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4}, Iff (Membership.mem.{u5, u5} M ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) (SetLike.instMembership.{u5, u5} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) M (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u5} L M _inst_1)) x (FunLike.coe.{succ u5, succ u5, succ u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (fun (_x : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) _x) (RelHomClass.toFunLike.{u5, u5, u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (FirstOrder.Language.LHom.substructureReduct.{u3, u4, u5, u2, u1} L M _inst_1 L' _inst_4 φ _inst_5) S)) (Membership.mem.{u5, u5} M (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (SetLike.instMembership.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u2, u1, u5} L' M _inst_4)) x S)
 Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.mem_substructure_reduct FirstOrder.Language.LHom.mem_substructureReductₓ'. -/
@@ -1195,7 +1195,7 @@ theorem mem_substructureReduct {x : M} {S : L'.Substructure M} :
 
 /- warning: first_order.language.Lhom.coe_substructure_reduct -> FirstOrder.Language.LHom.coe_substructureReduct is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4] {S : FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4}, Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, u4, u5} L M _inst_1 L' _inst_4 φ _inst_5) S)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) S)
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4] {S : FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4}, Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, u4, u5} L M _inst_1 L' _inst_4 φ _inst_5) S)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) S)
 but is expected to have type
   forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] {L' : FirstOrder.Language.{u2, u1}} [_inst_4 : FirstOrder.Language.Structure.{u2, u1, u5} L' M] (φ : FirstOrder.Language.LHom.{u3, u4, u2, u1} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u3, u4, u2, u1, u5} L L' φ M _inst_1 _inst_4] {S : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4}, Eq.{succ u5} (Set.{u5} M) (SetLike.coe.{u5, u5} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) M (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u5} L M _inst_1) (FunLike.coe.{succ u5, succ u5, succ u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (fun (_x : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) _x) (RelHomClass.toFunLike.{u5, u5, u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (FirstOrder.Language.LHom.substructureReduct.{u3, u4, u5, u2, u1} L M _inst_1 L' _inst_4 φ _inst_5) S)) (SetLike.coe.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u2, u1, u5} L' M _inst_4) S)
 Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.coe_substructure_reduct FirstOrder.Language.LHom.coe_substructureReductₓ'. -/
@@ -1240,7 +1240,7 @@ theorem coe_withConstants : (S.withConstants h : Set M) = ↑S :=
 
 /- warning: first_order.language.substructure.reduct_with_constants -> FirstOrder.Language.Substructure.reduct_withConstants is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {A : Set.{u3} M} (h : HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) A ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, max u1 u3, u2} L M _inst_1 (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)) (FirstOrder.Language.lhomWithConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) (FirstOrder.Language.withConstants_expansion.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) S
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {A : Set.{u3} M} (h : HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) A ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, max u1 u3, u2} L M _inst_1 (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)) (FirstOrder.Language.lhomWithConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) (FirstOrder.Language.withConstants_expansion.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) S
 but is expected to have type
   forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {A : Set.{u3} M} (h : HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) A (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S)), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (fun (_x : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) => LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) => LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, max u1 u3, u2} L M _inst_1 (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A)) (FirstOrder.Language.lhomWithConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) (FirstOrder.Language.withConstants_expansion.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) S
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.reduct_with_constants FirstOrder.Language.Substructure.reduct_withConstantsₓ'. -/
@@ -1399,7 +1399,7 @@ theorem range_comp (f : M →[L] N) (g : N →[L] P) : range (g.comp f : M →[L
 
 /- warning: first_order.language.hom.range_comp_le_range -> FirstOrder.Language.Hom.range_comp_le_range is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3), LE.le.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (SetLike.partialOrder.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)))) (FirstOrder.Language.Hom.range.{u1, u2, u3, u5} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f)) (FirstOrder.Language.Hom.range.{u1, u2, u4, u5} L N P _inst_2 _inst_3 g)
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3), LE.le.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (Preorder.toHasLe.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (SetLike.partialOrder.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)))) (FirstOrder.Language.Hom.range.{u1, u2, u3, u5} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f)) (FirstOrder.Language.Hom.range.{u1, u2, u4, u5} L N P _inst_2 _inst_3 g)
 but is expected to have type
   forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} {P : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u1} L P] (f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u3, u4, u2, u1} L N P _inst_2 _inst_3), LE.le.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u1} L P _inst_3))))) (FirstOrder.Language.Hom.range.{u3, u4, u5, u1} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 P _inst_3 g f)) (FirstOrder.Language.Hom.range.{u3, u4, u2, u1} L N P _inst_2 _inst_3 g)
 Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_comp_le_range FirstOrder.Language.Hom.range_comp_le_rangeₓ'. -/
@@ -1419,7 +1419,7 @@ theorem range_eq_top {f : M →[L] N} : range f = ⊤ ↔ Function.Surjective f
 
 /- warning: first_order.language.hom.range_le_iff_comap -> FirstOrder.Language.Hom.range_le_iff_comap is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p) (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1)))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p) (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1)))
 but is expected to have type
   forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2}, Iff (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p) (Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f p) (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1)))
 Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_le_iff_comap FirstOrder.Language.Hom.range_le_iff_comapₓ'. -/
@@ -1429,7 +1429,7 @@ theorem range_le_iff_comap {f : M →[L] N} {p : L.Substructure N} : range f ≤
 
 /- warning: first_order.language.hom.map_le_range -> FirstOrder.Language.Hom.map_le_range is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toHasLe.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
 but is expected to have type
   forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1}, LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f p) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)
 Case conversion may be inaccurate. Consider using '#align first_order.language.hom.map_le_range FirstOrder.Language.Hom.map_le_rangeₓ'. -/
@@ -1639,7 +1639,7 @@ namespace Substructure
 
 /- warning: first_order.language.substructure.inclusion -> FirstOrder.Language.Substructure.inclusion is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T) -> (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T) -> (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T))
 but is expected to have type
   forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S T) -> (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T))
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.inclusion FirstOrder.Language.Substructure.inclusionₓ'. -/
@@ -1650,7 +1650,7 @@ def inclusion {S T : L.Substructure M} (h : S ≤ T) : S ↪[L] T :=
 
 /- warning: first_order.language.substructure.coe_inclusion -> FirstOrder.Language.Substructure.coe_inclusion is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} (h : LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T), Eq.{succ u3} ((fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) -> (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T)) (FirstOrder.Language.Substructure.inclusion.{u1, u2, u3} L M _inst_1 S T h)) (coeFn.{succ u3, succ u3} (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) -> (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T)) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (FirstOrder.Language.Substructure.inclusion.{u1, u2, u3} L M _inst_1 S T h)) (Set.inclusion.{u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) x ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)) (fun (x : M) => Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) x ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) T)) h)
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} (h : LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toHasLe.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T), Eq.{succ u3} ((fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) -> (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T)) (FirstOrder.Language.Substructure.inclusion.{u1, u2, u3} L M _inst_1 S T h)) (coeFn.{succ u3, succ u3} (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) -> (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T)) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (FirstOrder.Language.Substructure.inclusion.{u1, u2, u3} L M _inst_1 S T h)) (Set.inclusion.{u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) x ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)) (fun (x : M) => Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) x ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) T)) h)
 but is expected to have type
   forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} (h : LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S T), Eq.{succ u3} (forall (a : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)), (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) a) (FunLike.coe.{succ u3, succ u3, succ u3} (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (fun (_x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) _x) (EmbeddingLike.toFunLike.{succ u3, succ u3, succ u3} (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Embedding.embeddingLike.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T))) (FirstOrder.Language.Substructure.inclusion.{u1, u2, u3} L M _inst_1 S T h)) (Set.inclusion.{u3} M (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) T) h)
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.coe_inclusion FirstOrder.Language.Substructure.coe_inclusionₓ'. -/

6cf59007

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -104,10 +104,10 @@ theorem inf (hs : ClosedUnder f s) (ht : ClosedUnder f t) : ClosedUnder f (s ⊓
 
 variable {S : Set (Set M)}
 
-#print FirstOrder.Language.ClosedUnder.infₛ /-
-theorem infₛ (hS : ∀ s, s ∈ S → ClosedUnder f s) : ClosedUnder f (infₛ S) := fun x h s hs =>
+#print FirstOrder.Language.ClosedUnder.sInf /-
+theorem sInf (hS : ∀ s, s ∈ S → ClosedUnder f s) : ClosedUnder f (sInf S) := fun x h s hs =>
   hS s hs x fun i => h i s hs
-#align first_order.language.closed_under.Inf FirstOrder.Language.ClosedUnder.infₛ
+#align first_order.language.closed_under.Inf FirstOrder.Language.ClosedUnder.sInf
 -/
 
 end ClosedUnder
@@ -256,60 +256,60 @@ instance : InfSet (L.Substructure M) :=
   ⟨fun s =>
     { carrier := ⋂ t ∈ s, ↑t
       fun_mem := fun n f =>
-        ClosedUnder.infₛ
+        ClosedUnder.sInf
           (by
             rintro _ ⟨t, rfl⟩
             by_cases h : t ∈ s
             · simpa [h] using t.fun_mem f
             · simp [h]) }⟩
 
-#print FirstOrder.Language.Substructure.coe_infₛ /-
+#print FirstOrder.Language.Substructure.coe_sInf /-
 @[simp, norm_cast]
-theorem coe_infₛ (S : Set (L.Substructure M)) :
-    ((infₛ S : L.Substructure M) : Set M) = ⋂ s ∈ S, ↑s :=
+theorem coe_sInf (S : Set (L.Substructure M)) :
+    ((sInf S : L.Substructure M) : Set M) = ⋂ s ∈ S, ↑s :=
   rfl
-#align first_order.language.substructure.coe_Inf FirstOrder.Language.Substructure.coe_infₛ
+#align first_order.language.substructure.coe_Inf FirstOrder.Language.Substructure.coe_sInf
 -/
 
-#print FirstOrder.Language.Substructure.mem_infₛ /-
-theorem mem_infₛ {S : Set (L.Substructure M)} {x : M} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p :=
-  Set.mem_interᵢ₂
-#align first_order.language.substructure.mem_Inf FirstOrder.Language.Substructure.mem_infₛ
+#print FirstOrder.Language.Substructure.mem_sInf /-
+theorem mem_sInf {S : Set (L.Substructure M)} {x : M} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p :=
+  Set.mem_iInter₂
+#align first_order.language.substructure.mem_Inf FirstOrder.Language.Substructure.mem_sInf
 -/
 
-/- warning: first_order.language.substructure.mem_infi -> FirstOrder.Language.Substructure.mem_infᵢ is a dubious translation:
+/- warning: first_order.language.substructure.mem_infi -> FirstOrder.Language.Substructure.mem_iInf is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} {S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)} {x : M}, Iff (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (infᵢ.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (S i))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} {S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)} {x : M}, Iff (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (iInf.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (S i))
 but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} {S : ι -> (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1)} {x : M}, Iff (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x (infᵢ.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u2, u3, u4} L M _inst_1) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x (S i))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_infᵢₓ'. -/
-theorem mem_infᵢ {ι : Sort _} {S : ι → L.Substructure M} {x : M} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i :=
-  by simp only [infᵢ, mem_Inf, Set.forall_range_iff]
-#align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_infᵢ
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} {S : ι -> (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1)} {x : M}, Iff (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x (iInf.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u2, u3, u4} L M _inst_1) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x (S i))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_iInfₓ'. -/
+theorem mem_iInf {ι : Sort _} {S : ι → L.Substructure M} {x : M} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i :=
+  by simp only [iInf, mem_Inf, Set.forall_range_iff]
+#align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_iInf
 
-/- warning: first_order.language.substructure.coe_infi -> FirstOrder.Language.Substructure.coe_infᵢ is a dubious translation:
+/- warning: first_order.language.substructure.coe_infi -> FirstOrder.Language.Substructure.coe_iInf is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} {S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)}, Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (infᵢ.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => S i))) (Set.interᵢ.{u3, u4} M ι (fun (i : ι) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (S i)))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} {S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)}, Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (iInf.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => S i))) (Set.iInter.{u3, u4} M ι (fun (i : ι) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (S i)))
 but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} {S : ι -> (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1)}, Eq.{succ u4} (Set.{u4} M) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (infᵢ.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u2, u3, u4} L M _inst_1) ι (fun (i : ι) => S i))) (Set.interᵢ.{u4, u1} M ι (fun (i : ι) => SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (S i)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.coe_infi FirstOrder.Language.Substructure.coe_infᵢₓ'. -/
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} {S : ι -> (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1)}, Eq.{succ u4} (Set.{u4} M) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (iInf.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u2, u3, u4} L M _inst_1) ι (fun (i : ι) => S i))) (Set.iInter.{u4, u1} M ι (fun (i : ι) => SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (S i)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.coe_infi FirstOrder.Language.Substructure.coe_iInfₓ'. -/
 @[simp, norm_cast]
-theorem coe_infᵢ {ι : Sort _} {S : ι → L.Substructure M} : (↑(⨅ i, S i) : Set M) = ⋂ i, S i := by
-  simp only [infᵢ, coe_Inf, Set.binterᵢ_range]
-#align first_order.language.substructure.coe_infi FirstOrder.Language.Substructure.coe_infᵢ
+theorem coe_iInf {ι : Sort _} {S : ι → L.Substructure M} : (↑(⨅ i, S i) : Set M) = ⋂ i, S i := by
+  simp only [iInf, coe_Inf, Set.biInter_range]
+#align first_order.language.substructure.coe_infi FirstOrder.Language.Substructure.coe_iInf
 
 /-- Substructures of a structure form a complete lattice. -/
 instance : CompleteLattice (L.Substructure M) :=
   {
     completeLatticeOfInf (L.Substructure M) fun s =>
       IsGLB.of_image (fun S T => show (S : Set M) ≤ T ↔ S ≤ T from SetLike.coe_subset_coe)
-        isGLB_binfᵢ with
+        isGLB_biInf with
     le := (· ≤ ·)
     lt := (· < ·)
     top := ⊤
     le_top := fun S x hx => mem_top x
     inf := (· ⊓ ·)
-    infₛ := InfSet.infₛ
+    sInf := InfSet.sInf
     le_inf := fun a b c ha hb x hx => ⟨ha hx, hb hx⟩
     inf_le_left := fun a b x => And.left
     inf_le_right := fun a b x => And.right }
@@ -324,15 +324,15 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure FirstOrder.Language.Substructure.closureₓ'. -/
 /-- The `L.substructure` generated by a set. -/
 def closure : LowerAdjoint (coe : L.Substructure M → Set M) :=
-  ⟨fun s => infₛ { S | s ⊆ S }, fun s S =>
-    ⟨Set.Subset.trans fun x hx => mem_infₛ.2 fun S hS => hS hx, fun h => infₛ_le h⟩⟩
+  ⟨fun s => sInf { S | s ⊆ S }, fun s S =>
+    ⟨Set.Subset.trans fun x hx => mem_sInf.2 fun S hS => hS hx, fun h => sInf_le h⟩⟩
 #align first_order.language.substructure.closure FirstOrder.Language.Substructure.closure
 
 variable {L} {s : Set M}
 
 #print FirstOrder.Language.Substructure.mem_closure /-
 theorem mem_closure {x : M} : x ∈ closure L s ↔ ∀ S : L.Substructure M, s ⊆ S → x ∈ S :=
-  mem_infₛ
+  mem_sInf
 #align first_order.language.substructure.mem_closure FirstOrder.Language.Substructure.mem_closure
 -/
 
@@ -400,7 +400,7 @@ theorem coe_closure_eq_range_term_realize :
   let S : L.substructure M := ⟨range (term.realize coe), fun n f x hx => _⟩
   · change _ = (S : Set M)
     rw [← SetLike.ext'_iff]
-    refine' closure_eq_of_le (fun x hx => ⟨var ⟨x, hx⟩, rfl⟩) (le_infₛ fun S' hS' => _)
+    refine' closure_eq_of_le (fun x hx => ⟨var ⟨x, hx⟩, rfl⟩) (le_sInf fun S' hS' => _)
     · rintro _ ⟨t, rfl⟩
       exact t.realize_mem _ fun i => hS' i.2
   · simp only [mem_range] at *
@@ -542,12 +542,12 @@ theorem closure_union (s t : Set M) : closure L (s ∪ t) = closure L s ⊔ clos
 
 /- warning: first_order.language.substructure.closure_Union -> FirstOrder.Language.Substructure.closure_unionᵢ is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} (s : ι -> (Set.{u3} M)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Set.unionᵢ.{u3, u4} M ι (fun (i : ι) => s i))) (supᵢ.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι (fun (i : ι) => coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (s i)))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} (s : ι -> (Set.{u3} M)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Set.iUnion.{u3, u4} M ι (fun (i : ι) => s i))) (iSup.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι (fun (i : ι) => coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (s i)))
 but is expected to have type
-  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} (s : ι -> (Set.{u4} M)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) (Set.unionᵢ.{u4, u1} M ι (fun (i : ι) => s i))) (supᵢ.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))) ι (fun (i : ι) => LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) (s i)))
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} (s : ι -> (Set.{u4} M)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) (Set.iUnion.{u4, u1} M ι (fun (i : ι) => s i))) (iSup.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))) ι (fun (i : ι) => LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) (s i)))
 Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_Union FirstOrder.Language.Substructure.closure_unionᵢₓ'. -/
 theorem closure_unionᵢ {ι} (s : ι → Set M) : closure L (⋃ i, s i) = ⨆ i, closure L (s i) :=
-  (Substructure.gi L M).gc.l_supᵢ
+  (Substructure.gi L M).gc.l_iSup
 #align first_order.language.substructure.closure_Union FirstOrder.Language.Substructure.closure_unionᵢ
 
 /- warning: first_order.language.substructure.small_bot -> FirstOrder.Language.Substructure.small_bot is a dubious translation:
@@ -783,16 +783,16 @@ theorem map_sup (S T : L.Substructure M) (f : M →[L] N) : (S ⊔ T).map f = S.
   (gc_map_comap f).l_sup
 #align first_order.language.substructure.map_sup FirstOrder.Language.Substructure.map_sup
 
-/- warning: first_order.language.substructure.map_supr -> FirstOrder.Language.Substructure.map_supᵢ is a dubious translation:
+/- warning: first_order.language.substructure.map_supr -> FirstOrder.Language.Substructure.map_iSup is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Sort.{u5}} (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (supᵢ.{u3, u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι s)) (supᵢ.{u4, u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (s i)))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Sort.{u5}} (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iSup.{u3, u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι s)) (iSup.{u4, u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (s i)))
 but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u1} L N] {ι : Sort.{u2}} (f : FirstOrder.Language.Hom.{u3, u4, u5, u1} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (supᵢ.{u5, u2} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι s)) (supᵢ.{u1, u2} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u1} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (s i)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_supᵢₓ'. -/
-theorem map_supᵢ {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure M) :
-    (supᵢ s).map f = ⨆ i, (s i).map f :=
-  (gc_map_comap f).l_supᵢ
-#align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_supᵢ
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u1} L N] {ι : Sort.{u2}} (f : FirstOrder.Language.Hom.{u3, u4, u5, u1} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (iSup.{u5, u2} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι s)) (iSup.{u1, u2} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u1} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (s i)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_iSupₓ'. -/
+theorem map_iSup {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure M) :
+    (iSup s).map f = ⨆ i, (s i).map f :=
+  (gc_map_comap f).l_iSup
+#align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_iSup
 
 /- warning: first_order.language.substructure.comap_inf -> FirstOrder.Language.Substructure.comap_inf is a dubious translation:
 lean 3 declaration is
@@ -805,16 +805,16 @@ theorem comap_inf (S T : L.Substructure N) (f : M →[L] N) :
   (gc_map_comap f).u_inf
 #align first_order.language.substructure.comap_inf FirstOrder.Language.Substructure.comap_inf
 
-/- warning: first_order.language.substructure.comap_infi -> FirstOrder.Language.Substructure.comap_infᵢ is a dubious translation:
+/- warning: first_order.language.substructure.comap_infi -> FirstOrder.Language.Substructure.comap_iInf is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Sort.{u5}} (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (infᵢ.{u4, u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι s)) (infᵢ.{u3, u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (s i)))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Sort.{u5}} (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iInf.{u4, u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι s)) (iInf.{u3, u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (s i)))
 but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u1} L N] {ι : Sort.{u2}} (f : FirstOrder.Language.Hom.{u3, u4, u5, u1} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (infᵢ.{u1, u2} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u1} L N _inst_2) ι s)) (infᵢ.{u5, u2} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (s i)))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_infᵢₓ'. -/
-theorem comap_infᵢ {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure N) :
-    (infᵢ s).comap f = ⨅ i, (s i).comap f :=
-  (gc_map_comap f).u_infᵢ
-#align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_infᵢ
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u1} L N] {ι : Sort.{u2}} (f : FirstOrder.Language.Hom.{u3, u4, u5, u1} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (iInf.{u1, u2} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u1} L N _inst_2) ι s)) (iInf.{u5, u2} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (s i)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_iInfₓ'. -/
+theorem comap_iInf {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure N) :
+    (iInf s).comap f = ⨅ i, (s i).comap f :=
+  (gc_map_comap f).u_iInf
+#align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_iInf
 
 /- warning: first_order.language.substructure.map_bot -> FirstOrder.Language.Substructure.map_bot is a dubious translation:
 lean 3 declaration is
@@ -925,16 +925,16 @@ theorem comap_inf_map_of_injective (S T : L.Substructure M) : (S.map f ⊓ T.map
   (gciMapComap hf).u_inf_l _ _
 #align first_order.language.substructure.comap_inf_map_of_injective FirstOrder.Language.Substructure.comap_inf_map_of_injective
 
-/- warning: first_order.language.substructure.comap_infi_map_of_injective -> FirstOrder.Language.Substructure.comap_infᵢ_map_of_injective is a dubious translation:
+/- warning: first_order.language.substructure.comap_infi_map_of_injective -> FirstOrder.Language.Substructure.comap_iInf_map_of_injective is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (infᵢ.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (infᵢ.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι S))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iInf.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (iInf.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι S))
 but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Injective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (infᵢ.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u2} L N _inst_2) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (infᵢ.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι S))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_infi_map_of_injective FirstOrder.Language.Substructure.comap_infᵢ_map_of_injectiveₓ'. -/
-theorem comap_infᵢ_map_of_injective (S : ι → L.Substructure M) :
-    (⨅ i, (S i).map f).comap f = infᵢ S :=
-  (gciMapComap hf).u_infᵢ_l _
-#align first_order.language.substructure.comap_infi_map_of_injective FirstOrder.Language.Substructure.comap_infᵢ_map_of_injective
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Injective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (iInf.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u2} L N _inst_2) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (iInf.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι S))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_infi_map_of_injective FirstOrder.Language.Substructure.comap_iInf_map_of_injectiveₓ'. -/
+theorem comap_iInf_map_of_injective (S : ι → L.Substructure M) :
+    (⨅ i, (S i).map f).comap f = iInf S :=
+  (gciMapComap hf).u_iInf_l _
+#align first_order.language.substructure.comap_infi_map_of_injective FirstOrder.Language.Substructure.comap_iInf_map_of_injective
 
 /- warning: first_order.language.substructure.comap_sup_map_of_injective -> FirstOrder.Language.Substructure.comap_sup_map_of_injective is a dubious translation:
 lean 3 declaration is
@@ -946,16 +946,16 @@ theorem comap_sup_map_of_injective (S T : L.Substructure M) : (S.map f ⊔ T.map
   (gciMapComap hf).u_sup_l _ _
 #align first_order.language.substructure.comap_sup_map_of_injective FirstOrder.Language.Substructure.comap_sup_map_of_injective
 
-/- warning: first_order.language.substructure.comap_supr_map_of_injective -> FirstOrder.Language.Substructure.comap_supᵢ_map_of_injective is a dubious translation:
+/- warning: first_order.language.substructure.comap_supr_map_of_injective -> FirstOrder.Language.Substructure.comap_iSup_map_of_injective is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (supᵢ.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (supᵢ.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι S))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iSup.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (iSup.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι S))
 but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Injective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (supᵢ.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u2} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (supᵢ.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι S))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_supr_map_of_injective FirstOrder.Language.Substructure.comap_supᵢ_map_of_injectiveₓ'. -/
-theorem comap_supᵢ_map_of_injective (S : ι → L.Substructure M) :
-    (⨆ i, (S i).map f).comap f = supᵢ S :=
-  (gciMapComap hf).u_supᵢ_l _
-#align first_order.language.substructure.comap_supr_map_of_injective FirstOrder.Language.Substructure.comap_supᵢ_map_of_injective
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Injective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (iSup.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u2} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (iSup.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι S))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_supr_map_of_injective FirstOrder.Language.Substructure.comap_iSup_map_of_injectiveₓ'. -/
+theorem comap_iSup_map_of_injective (S : ι → L.Substructure M) :
+    (⨆ i, (S i).map f).comap f = iSup S :=
+  (gciMapComap hf).u_iSup_l _
+#align first_order.language.substructure.comap_supr_map_of_injective FirstOrder.Language.Substructure.comap_iSup_map_of_injective
 
 /- warning: first_order.language.substructure.map_le_map_iff_of_injective -> FirstOrder.Language.Substructure.map_le_map_iff_of_injective is a dubious translation:
 lean 3 declaration is
@@ -1039,16 +1039,16 @@ theorem map_inf_comap_of_surjective (S T : L.Substructure N) :
   (giMapComap hf).l_inf_u _ _
 #align first_order.language.substructure.map_inf_comap_of_surjective FirstOrder.Language.Substructure.map_inf_comap_of_surjective
 
-/- warning: first_order.language.substructure.map_infi_comap_of_surjective -> FirstOrder.Language.Substructure.map_infᵢ_comap_of_surjective is a dubious translation:
+/- warning: first_order.language.substructure.map_infi_comap_of_surjective -> FirstOrder.Language.Substructure.map_iInf_comap_of_surjective is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (infᵢ.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (infᵢ.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι S))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iInf.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (iInf.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι S))
 but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2)), Eq.{succ u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (infᵢ.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (infᵢ.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u2} L N _inst_2) ι S))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_infi_comap_of_surjective FirstOrder.Language.Substructure.map_infᵢ_comap_of_surjectiveₓ'. -/
-theorem map_infᵢ_comap_of_surjective (S : ι → L.Substructure N) :
-    (⨅ i, (S i).comap f).map f = infᵢ S :=
-  (giMapComap hf).l_infᵢ_u _
-#align first_order.language.substructure.map_infi_comap_of_surjective FirstOrder.Language.Substructure.map_infᵢ_comap_of_surjective
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2)), Eq.{succ u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (iInf.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (iInf.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u2} L N _inst_2) ι S))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_infi_comap_of_surjective FirstOrder.Language.Substructure.map_iInf_comap_of_surjectiveₓ'. -/
+theorem map_iInf_comap_of_surjective (S : ι → L.Substructure N) :
+    (⨅ i, (S i).comap f).map f = iInf S :=
+  (giMapComap hf).l_iInf_u _
+#align first_order.language.substructure.map_infi_comap_of_surjective FirstOrder.Language.Substructure.map_iInf_comap_of_surjective
 
 /- warning: first_order.language.substructure.map_sup_comap_of_surjective -> FirstOrder.Language.Substructure.map_sup_comap_of_surjective is a dubious translation:
 lean 3 declaration is
@@ -1061,16 +1061,16 @@ theorem map_sup_comap_of_surjective (S T : L.Substructure N) :
   (giMapComap hf).l_sup_u _ _
 #align first_order.language.substructure.map_sup_comap_of_surjective FirstOrder.Language.Substructure.map_sup_comap_of_surjective
 
-/- warning: first_order.language.substructure.map_supr_comap_of_surjective -> FirstOrder.Language.Substructure.map_supᵢ_comap_of_surjective is a dubious translation:
+/- warning: first_order.language.substructure.map_supr_comap_of_surjective -> FirstOrder.Language.Substructure.map_iSup_comap_of_surjective is a dubious translation:
 lean 3 declaration is
-  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (supᵢ.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (supᵢ.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι S))
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (iSup.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (iSup.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι S))
 but is expected to have type
-  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2)), Eq.{succ u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (supᵢ.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (supᵢ.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u2} L N _inst_2))) ι S))
-Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_supr_comap_of_surjective FirstOrder.Language.Substructure.map_supᵢ_comap_of_surjectiveₓ'. -/
-theorem map_supᵢ_comap_of_surjective (S : ι → L.Substructure N) :
-    (⨆ i, (S i).comap f).map f = supᵢ S :=
-  (giMapComap hf).l_supᵢ_u _
-#align first_order.language.substructure.map_supr_comap_of_surjective FirstOrder.Language.Substructure.map_supᵢ_comap_of_surjective
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2)), Eq.{succ u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (iSup.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (iSup.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u2} L N _inst_2))) ι S))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_supr_comap_of_surjective FirstOrder.Language.Substructure.map_iSup_comap_of_surjectiveₓ'. -/
+theorem map_iSup_comap_of_surjective (S : ι → L.Substructure N) :
+    (⨆ i, (S i).comap f).map f = iSup S :=
+  (giMapComap hf).l_iSup_u _
+#align first_order.language.substructure.map_supr_comap_of_surjective FirstOrder.Language.Substructure.map_iSup_comap_of_surjective
 
 /- warning: first_order.language.substructure.comap_le_comap_iff_of_surjective -> FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjective is a dubious translation:
 lean 3 declaration is

6cf59007

bump to nightly-2023-05-14-02

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

fbb256bf

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 
 ! This file was ported from Lean 3 source module model_theory.substructures
-! leanprover-community/mathlib commit 0602c59878ff3d5f71dea69c2d32ccf2e93e5398
+! leanprover-community/mathlib commit 6cf5900728239efa287df7761ec2a1ac9cf39b29
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.ModelTheory.Encoding
 
 /-!
 # First-Order Substructures
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 This file defines substructures of first-order structures in a similar manner to the various
 substructures appearing in the algebra library.

0602c598

bump to nightly-2023-05-12-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

1d98000d

Diff

@@ -60,34 +60,52 @@ open Set
 
 variable {n : ℕ} (f : L.Functions n) (s : Set M)
 
+#print FirstOrder.Language.ClosedUnder /-
 /-- Indicates that a set in a given structure is a closed under a function symbol. -/
 def ClosedUnder : Prop :=
   ∀ x : Fin n → M, (∀ i : Fin n, x i ∈ s) → funMap f x ∈ s
 #align first_order.language.closed_under FirstOrder.Language.ClosedUnder
+-/
 
 variable (L)
 
+#print FirstOrder.Language.closedUnder_univ /-
 @[simp]
 theorem closedUnder_univ : ClosedUnder f (univ : Set M) := fun _ _ => mem_univ _
 #align first_order.language.closed_under_univ FirstOrder.Language.closedUnder_univ
+-/
 
 variable {L f s} {t : Set M}
 
 namespace ClosedUnder
 
+/- warning: first_order.language.closed_under.inter -> FirstOrder.Language.ClosedUnder.inter is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {n : Nat} {f : FirstOrder.Language.Functions.{u1, u2} L n} {s : Set.{u3} M} {t : Set.{u3} M}, (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f s) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f t) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f (Inter.inter.{u3} (Set.{u3} M) (Set.hasInter.{u3} M) s t))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {n : Nat} {f : FirstOrder.Language.Functions.{u1, u2} L n} {s : Set.{u3} M} {t : Set.{u3} M}, (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f s) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f t) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f (Inter.inter.{u3} (Set.{u3} M) (Set.instInterSet.{u3} M) s t))
+Case conversion may be inaccurate. Consider using '#align first_order.language.closed_under.inter FirstOrder.Language.ClosedUnder.interₓ'. -/
 theorem inter (hs : ClosedUnder f s) (ht : ClosedUnder f t) : ClosedUnder f (s ∩ t) := fun x h =>
   mem_inter (hs x fun i => mem_of_mem_inter_left (h i)) (ht x fun i => mem_of_mem_inter_right (h i))
 #align first_order.language.closed_under.inter FirstOrder.Language.ClosedUnder.inter
 
+/- warning: first_order.language.closed_under.inf -> FirstOrder.Language.ClosedUnder.inf is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {n : Nat} {f : FirstOrder.Language.Functions.{u1, u2} L n} {s : Set.{u3} M} {t : Set.{u3} M}, (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f s) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f t) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f (Inf.inf.{u3} (Set.{u3} M) (SemilatticeInf.toHasInf.{u3} (Set.{u3} M) (Lattice.toSemilatticeInf.{u3} (Set.{u3} M) (ConditionallyCompleteLattice.toLattice.{u3} (Set.{u3} M) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M)))))))) s t))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {n : Nat} {f : FirstOrder.Language.Functions.{u1, u2} L n} {s : Set.{u3} M} {t : Set.{u3} M}, (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f s) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f t) -> (FirstOrder.Language.ClosedUnder.{u1, u2, u3} L M _inst_1 n f (Inf.inf.{u3} (Set.{u3} M) (Lattice.toInf.{u3} (Set.{u3} M) (ConditionallyCompleteLattice.toLattice.{u3} (Set.{u3} M) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) s t))
+Case conversion may be inaccurate. Consider using '#align first_order.language.closed_under.inf FirstOrder.Language.ClosedUnder.infₓ'. -/
 theorem inf (hs : ClosedUnder f s) (ht : ClosedUnder f t) : ClosedUnder f (s ⊓ t) :=
   hs.inter ht
 #align first_order.language.closed_under.inf FirstOrder.Language.ClosedUnder.inf
 
 variable {S : Set (Set M)}
 
+#print FirstOrder.Language.ClosedUnder.infₛ /-
 theorem infₛ (hS : ∀ s, s ∈ S → ClosedUnder f s) : ClosedUnder f (infₛ S) := fun x h s hs =>
   hS s hs x fun i => h i s hs
 #align first_order.language.closed_under.Inf FirstOrder.Language.ClosedUnder.infₛ
+-/
 
 end ClosedUnder
 
@@ -95,11 +113,13 @@ end ClosedUnder
 
 variable (L) (M)
 
+#print FirstOrder.Language.Substructure /-
 /-- A substructure of a structure `M` is a set closed under application of function symbols. -/
 structure Substructure where
   carrier : Set M
   fun_mem : ∀ {n}, ∀ f : L.Functions n, ClosedUnder f carrier
 #align first_order.language.substructure FirstOrder.Language.Substructure
+-/
 
 variable {L} {M}
 
@@ -108,35 +128,49 @@ namespace Substructure
 instance : SetLike (L.Substructure M) M :=
   ⟨Substructure.carrier, fun p q h => by cases p <;> cases q <;> congr ⟩
 
+#print FirstOrder.Language.Substructure.Simps.coe /-
 /-- See Note [custom simps projection] -/
 def Simps.coe (S : L.Substructure M) : Set M :=
   S
 #align first_order.language.substructure.simps.coe FirstOrder.Language.Substructure.Simps.coe
+-/
 
 initialize_simps_projections Substructure (carrier → coe)
 
+#print FirstOrder.Language.Substructure.mem_carrier /-
 @[simp]
 theorem mem_carrier {s : L.Substructure M} {x : M} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align first_order.language.substructure.mem_carrier FirstOrder.Language.Substructure.mem_carrier
+-/
 
+#print FirstOrder.Language.Substructure.ext /-
 /-- Two substructures are equal if they have the same elements. -/
 @[ext]
 theorem ext {S T : L.Substructure M} (h : ∀ x, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
 #align first_order.language.substructure.ext FirstOrder.Language.Substructure.ext
+-/
 
+#print FirstOrder.Language.Substructure.copy /-
 /-- Copy a substructure replacing `carrier` with a set that is equal to it. -/
 protected def copy (S : L.Substructure M) (s : Set M) (hs : s = S) : L.Substructure M
     where
   carrier := s
   fun_mem n f := hs.symm ▸ S.fun_mem f
 #align first_order.language.substructure.copy FirstOrder.Language.Substructure.copy
+-/
 
 end Substructure
 
 variable {S : L.Substructure M}
 
+/- warning: first_order.language.term.realize_mem -> FirstOrder.Language.Term.realize_mem is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {α : Type.{u4}} (t : FirstOrder.Language.Term.{u1, u2, u4} L α) (xs : α -> M), (forall (a : α), Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (xs a) S) -> (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Term.realize.{u1, u2, u3, u4} L M _inst_1 α xs t) S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {α : Type.{u1}} (t : FirstOrder.Language.Term.{u2, u3, u1} L α) (xs : α -> M), (forall (a : α), Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (xs a) S) -> (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Term.realize.{u2, u3, u4, u1} L M _inst_1 α xs t) S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.term.realize_mem FirstOrder.Language.Term.realize_memₓ'. -/
 theorem Term.realize_mem {α : Type _} (t : L.term α) (xs : α → M) (h : ∀ a, xs a ∈ S) :
     t.realize xs ∈ S := by
   induction' t with a n f ts ih
@@ -146,15 +180,25 @@ theorem Term.realize_mem {α : Type _} (t : L.term α) (xs : α → M) (h : ∀
 
 namespace Substructure
 
+#print FirstOrder.Language.Substructure.coe_copy /-
 @[simp]
 theorem coe_copy {s : Set M} (hs : s = S) : (S.copy s hs : Set M) = s :=
   rfl
 #align first_order.language.substructure.coe_copy FirstOrder.Language.Substructure.coe_copy
+-/
 
+#print FirstOrder.Language.Substructure.copy_eq /-
 theorem copy_eq {s : Set M} (hs : s = S) : S.copy s hs = S :=
   SetLike.coe_injective hs
 #align first_order.language.substructure.copy_eq FirstOrder.Language.Substructure.copy_eq
+-/
 
+/- warning: first_order.language.substructure.constants_mem -> FirstOrder.Language.Substructure.constants_mem is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} (c : FirstOrder.Language.Constants.{u1, u2} L), Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) ((fun (a : Type.{u1}) (b : Type.{u3}) [self : HasLiftT.{succ u1, succ u3} a b] => self.0) (FirstOrder.Language.Constants.{u1, u2} L) M (HasLiftT.mk.{succ u1, succ u3} (FirstOrder.Language.Constants.{u1, u2} L) M (CoeTCₓ.coe.{succ u1, succ u3} (FirstOrder.Language.Constants.{u1, u2} L) M (FirstOrder.Language.hasCoeT.{u1, u2, u3} L M _inst_1))) c) S
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} (c : FirstOrder.Language.Constants.{u1, u2} L), Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.constantMap.{u1, u2, u3} L M _inst_1 c) S
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.constants_mem FirstOrder.Language.Substructure.constants_memₓ'. -/
 theorem constants_mem (c : L.Constants) : ↑c ∈ S :=
   mem_carrier.2 (S.fun_mem c _ Fin.elim0)
 #align first_order.language.substructure.constants_mem FirstOrder.Language.Substructure.constants_mem
@@ -167,15 +211,19 @@ instance : Top (L.Substructure M) :=
 instance : Inhabited (L.Substructure M) :=
   ⟨⊤⟩
 
+#print FirstOrder.Language.Substructure.mem_top /-
 @[simp]
 theorem mem_top (x : M) : x ∈ (⊤ : L.Substructure M) :=
   Set.mem_univ x
 #align first_order.language.substructure.mem_top FirstOrder.Language.Substructure.mem_top
+-/
 
+#print FirstOrder.Language.Substructure.coe_top /-
 @[simp]
 theorem coe_top : ((⊤ : L.Substructure M) : Set M) = Set.univ :=
   rfl
 #align first_order.language.substructure.coe_top FirstOrder.Language.Substructure.coe_top
+-/
 
 /-- The inf of two substructures is their intersection. -/
 instance : Inf (L.Substructure M) :=
@@ -183,15 +231,23 @@ instance : Inf (L.Substructure M) :=
     { carrier := S₁ ∩ S₂
       fun_mem := fun n f => (S₁.fun_mem f).inf (S₂.fun_mem f) }⟩
 
+/- warning: first_order.language.substructure.coe_inf -> FirstOrder.Language.Substructure.coe_inf is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] (p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (p' : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1), Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (Inf.inf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u1, u2, u3} L M _inst_1) p p')) (Inter.inter.{u3} (Set.{u3} M) (Set.hasInter.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) p) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) p'))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] (p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (p' : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1), Eq.{succ u3} (Set.{u3} M) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) (Inf.inf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u1, u2, u3} L M _inst_1) p p')) (Inter.inter.{u3} (Set.{u3} M) (Set.instInterSet.{u3} M) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) p) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) p'))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.coe_inf FirstOrder.Language.Substructure.coe_infₓ'. -/
 @[simp]
 theorem coe_inf (p p' : L.Substructure M) : ((p ⊓ p' : L.Substructure M) : Set M) = p ∩ p' :=
   rfl
 #align first_order.language.substructure.coe_inf FirstOrder.Language.Substructure.coe_inf
 
+#print FirstOrder.Language.Substructure.mem_inf /-
 @[simp]
 theorem mem_inf {p p' : L.Substructure M} {x : M} : x ∈ p ⊓ p' ↔ x ∈ p ∧ x ∈ p' :=
   Iff.rfl
 #align first_order.language.substructure.mem_inf FirstOrder.Language.Substructure.mem_inf
+-/
 
 instance : InfSet (L.Substructure M) :=
   ⟨fun s =>
@@ -204,20 +260,36 @@ instance : InfSet (L.Substructure M) :=
             · simpa [h] using t.fun_mem f
             · simp [h]) }⟩
 
+#print FirstOrder.Language.Substructure.coe_infₛ /-
 @[simp, norm_cast]
 theorem coe_infₛ (S : Set (L.Substructure M)) :
     ((infₛ S : L.Substructure M) : Set M) = ⋂ s ∈ S, ↑s :=
   rfl
 #align first_order.language.substructure.coe_Inf FirstOrder.Language.Substructure.coe_infₛ
+-/
 
+#print FirstOrder.Language.Substructure.mem_infₛ /-
 theorem mem_infₛ {S : Set (L.Substructure M)} {x : M} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p :=
   Set.mem_interᵢ₂
 #align first_order.language.substructure.mem_Inf FirstOrder.Language.Substructure.mem_infₛ
+-/
 
+/- warning: first_order.language.substructure.mem_infi -> FirstOrder.Language.Substructure.mem_infᵢ is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} {S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)} {x : M}, Iff (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (infᵢ.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (S i))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} {S : ι -> (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1)} {x : M}, Iff (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x (infᵢ.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u2, u3, u4} L M _inst_1) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x (S i))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_infᵢₓ'. -/
 theorem mem_infᵢ {ι : Sort _} {S : ι → L.Substructure M} {x : M} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i :=
   by simp only [infᵢ, mem_Inf, Set.forall_range_iff]
 #align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_infᵢ
 
+/- warning: first_order.language.substructure.coe_infi -> FirstOrder.Language.Substructure.coe_infᵢ is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} {S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)}, Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (infᵢ.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => S i))) (Set.interᵢ.{u3, u4} M ι (fun (i : ι) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (S i)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} {S : ι -> (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1)}, Eq.{succ u4} (Set.{u4} M) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (infᵢ.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u2, u3, u4} L M _inst_1) ι (fun (i : ι) => S i))) (Set.interᵢ.{u4, u1} M ι (fun (i : ι) => SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (S i)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.coe_infi FirstOrder.Language.Substructure.coe_infᵢₓ'. -/
 @[simp, norm_cast]
 theorem coe_infᵢ {ι : Sort _} {S : ι → L.Substructure M} : (↑(⨅ i, S i) : Set M) = ⋂ i, S i := by
   simp only [infᵢ, coe_Inf, Set.binterᵢ_range]
@@ -241,6 +313,12 @@ instance : CompleteLattice (L.Substructure M) :=
 
 variable (L)
 
+/- warning: first_order.language.substructure.closure -> FirstOrder.Language.Substructure.closure is a dubious translation:
+lean 3 declaration is
+  forall (L : FirstOrder.Language.{u1, u2}) {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))
+but is expected to have type
+  forall (L : FirstOrder.Language.{u1, u2}) {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure FirstOrder.Language.Substructure.closureₓ'. -/
 /-- The `L.substructure` generated by a set. -/
 def closure : LowerAdjoint (coe : L.Substructure M → Set M) :=
   ⟨fun s => infₛ { S | s ⊆ S }, fun s S =>
@@ -249,43 +327,70 @@ def closure : LowerAdjoint (coe : L.Substructure M → Set M) :=
 
 variable {L} {s : Set M}
 
+#print FirstOrder.Language.Substructure.mem_closure /-
 theorem mem_closure {x : M} : x ∈ closure L s ↔ ∀ S : L.Substructure M, s ⊆ S → x ∈ S :=
   mem_infₛ
 #align first_order.language.substructure.mem_closure FirstOrder.Language.Substructure.mem_closure
+-/
 
+#print FirstOrder.Language.Substructure.subset_closure /-
 /-- The substructure generated by a set includes the set. -/
 @[simp]
 theorem subset_closure : s ⊆ closure L s :=
   (closure L).le_closure s
 #align first_order.language.substructure.subset_closure FirstOrder.Language.Substructure.subset_closure
+-/
 
+#print FirstOrder.Language.Substructure.not_mem_of_not_mem_closure /-
 theorem not_mem_of_not_mem_closure {P : M} (hP : P ∉ closure L s) : P ∉ s := fun h =>
   hP (subset_closure h)
 #align first_order.language.substructure.not_mem_of_not_mem_closure FirstOrder.Language.Substructure.not_mem_of_not_mem_closure
+-/
 
+#print FirstOrder.Language.Substructure.closed /-
 @[simp]
 theorem closed (S : L.Substructure M) : (closure L).closed (S : Set M) :=
   congr rfl ((closure L).eq_of_le Set.Subset.rfl fun x xS => mem_closure.2 fun T hT => hT xS)
 #align first_order.language.substructure.closed FirstOrder.Language.Substructure.closed
+-/
 
 open Set
 
+/- warning: first_order.language.substructure.closure_le -> FirstOrder.Language.Substructure.closure_le is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, Iff (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S) (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, Iff (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S) (HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) s (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_le FirstOrder.Language.Substructure.closure_leₓ'. -/
 /-- A substructure `S` includes `closure L s` if and only if it includes `s`. -/
 @[simp]
 theorem closure_le : closure L s ≤ S ↔ s ⊆ S :=
   (closure L).closure_le_closed_iff_le s S.closed
 #align first_order.language.substructure.closure_le FirstOrder.Language.Substructure.closure_le
 
+/- warning: first_order.language.substructure.closure_mono -> FirstOrder.Language.Substructure.closure_mono is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {{s : Set.{u3} M}} {{t : Set.{u3} M}}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s t) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) t))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {{s : Set.{u3} M}} {{t : Set.{u3} M}}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) s t) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) t))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_mono FirstOrder.Language.Substructure.closure_monoₓ'. -/
 /-- Substructure closure of a set is monotone in its argument: if `s ⊆ t`,
 then `closure L s ≤ closure L t`. -/
 theorem closure_mono ⦃s t : Set M⦄ (h : s ⊆ t) : closure L s ≤ closure L t :=
   (closure L).Monotone h
 #align first_order.language.substructure.closure_mono FirstOrder.Language.Substructure.closure_mono
 
+/- warning: first_order.language.substructure.closure_eq_of_le -> FirstOrder.Language.Substructure.closure_eq_of_le is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)) -> (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {s : Set.{u3} M}, (HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) s (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S)) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)) -> (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_eq_of_le FirstOrder.Language.Substructure.closure_eq_of_leₓ'. -/
 theorem closure_eq_of_le (h₁ : s ⊆ S) (h₂ : S ≤ closure L s) : closure L s = S :=
   (closure L).eq_of_le h₁ h₂
 #align first_order.language.substructure.closure_eq_of_le FirstOrder.Language.Substructure.closure_eq_of_le
 
+#print FirstOrder.Language.Substructure.coe_closure_eq_range_term_realize /-
 theorem coe_closure_eq_range_term_realize :
     (closure L s : Set M) = range (@Term.realize L _ _ _ (coe : s → M)) :=
   by
@@ -299,25 +404,38 @@ theorem coe_closure_eq_range_term_realize :
     refine' ⟨func f fun i => Classical.choose (hx i), _⟩
     simp only [term.realize, fun i => Classical.choose_spec (hx i)]
 #align first_order.language.substructure.coe_closure_eq_range_term_realize FirstOrder.Language.Substructure.coe_closure_eq_range_term_realize
+-/
 
+#print FirstOrder.Language.Substructure.small_closure /-
 instance small_closure [Small.{u} s] : Small.{u} (closure L s) :=
   by
   rw [← SetLike.coe_sort_coe, substructure.coe_closure_eq_range_term_realize]
   exact small_range _
 #align first_order.language.substructure.small_closure FirstOrder.Language.Substructure.small_closure
+-/
 
+#print FirstOrder.Language.Substructure.mem_closure_iff_exists_term /-
 theorem mem_closure_iff_exists_term {x : M} :
     x ∈ closure L s ↔ ∃ t : L.term s, t.realize (coe : s → M) = x := by
   rw [← SetLike.mem_coe, coe_closure_eq_range_term_realize, mem_range]
 #align first_order.language.substructure.mem_closure_iff_exists_term FirstOrder.Language.Substructure.mem_closure_iff_exists_term
+-/
 
+#print FirstOrder.Language.Substructure.lift_card_closure_le_card_term /-
 theorem lift_card_closure_le_card_term : Cardinal.lift.{max u w} (#closure L s) ≤ (#L.term s) :=
   by
   rw [← SetLike.coe_sort_coe, coe_closure_eq_range_term_realize]
   rw [← Cardinal.lift_id'.{w, max u w} (#L.term s)]
   exact Cardinal.mk_range_le_lift
 #align first_order.language.substructure.lift_card_closure_le_card_term FirstOrder.Language.Substructure.lift_card_closure_le_card_term
+-/
 
+/- warning: first_order.language.substructure.lift_card_closure_le -> FirstOrder.Language.Substructure.lift_card_closure_le is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {s : Set.{u3} M}, LE.le.{succ (max u3 u1)} Cardinal.{max u3 u1} Cardinal.hasLe.{max u3 u1} (Cardinal.lift.{u1, u3} (Cardinal.mk.{u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)))) (LinearOrder.max.{succ (max u3 u1)} Cardinal.{max u3 u1} Cardinal.linearOrder.{max u3 u1} Cardinal.aleph0.{max u3 u1} (HAdd.hAdd.{succ (max u3 u1), succ (max u3 u1), succ (max u3 u1)} Cardinal.{max u3 u1} Cardinal.{max u3 u1} Cardinal.{max u3 u1} (instHAdd.{succ (max u3 u1)} Cardinal.{max u3 u1} Cardinal.hasAdd.{max u3 u1}) (Cardinal.lift.{u1, u3} (Cardinal.mk.{u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) s))) (Cardinal.lift.{u3, u1} (Cardinal.mk.{u1} (Sigma.{0, u1} Nat (fun (i : Nat) => FirstOrder.Language.Functions.{u1, u2} L i))))))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {s : Set.{u3} M}, LE.le.{max (succ u1) (succ u3)} Cardinal.{max u3 u1} Cardinal.instLECardinal.{max u1 u3} (Cardinal.lift.{u1, u3} (Cardinal.mk.{u3} (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s))))) (Max.max.{succ (max u1 u3)} Cardinal.{max u1 u3} (CanonicallyLinearOrderedAddMonoid.toMax.{max (succ u1) (succ u3)} Cardinal.{max u1 u3} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{max u1 u3}) Cardinal.aleph0.{max u1 u3} (HAdd.hAdd.{max (succ u1) (succ u3), max (succ u1) (succ u3), max (succ u1) (succ u3)} Cardinal.{max u3 u1} Cardinal.{max u1 u3} Cardinal.{max u3 u1} (instHAdd.{max (succ u1) (succ u3)} Cardinal.{max u3 u1} Cardinal.instAddCardinal.{max u1 u3}) (Cardinal.lift.{u1, u3} (Cardinal.mk.{u3} (Set.Elem.{u3} M s))) (Cardinal.lift.{u3, u1} (Cardinal.mk.{u1} (Sigma.{0, u1} Nat (fun (i : Nat) => FirstOrder.Language.Functions.{u1, u2} L i))))))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.lift_card_closure_le FirstOrder.Language.Substructure.lift_card_closure_leₓ'. -/
 theorem lift_card_closure_le :
     Cardinal.lift.{u, w} (#closure L s) ≤
       max ℵ₀ (Cardinal.lift.{u, w} (#s) + Cardinal.lift.{w, u} (#Σi, L.Functions i)) :=
@@ -329,6 +447,7 @@ theorem lift_card_closure_le :
 
 variable (L)
 
+#print Set.Countable.substructure_closure /-
 theorem Set.Countable.substructure_closure [Countable (Σl, L.Functions l)] (h : s.Countable) :
     Countable.{w + 1} (closure L s) :=
   by
@@ -336,9 +455,11 @@ theorem Set.Countable.substructure_closure [Countable (Σl, L.Functions l)] (h :
   rw [← mk_le_aleph_0_iff, ← lift_le_aleph_0]
   exact lift_card_closure_le_card_term.trans mk_le_aleph_0
 #align set.countable.substructure_closure Set.Countable.substructure_closure
+-/
 
 variable {L} (S)
 
+#print FirstOrder.Language.Substructure.closure_induction /-
 /-- An induction principle for closure membership. If `p` holds for all elements of `s`, and
 is preserved under function symbols, then `p` holds for all elements of the closure of `s`. -/
 @[elab_as_elim]
@@ -346,7 +467,9 @@ theorem closure_induction {p : M → Prop} {x} (h : x ∈ closure L s) (Hs : ∀
     (Hfun : ∀ {n : ℕ} (f : L.Functions n), ClosedUnder f (setOf p)) : p x :=
   (@closure_le L M _ ⟨setOf p, fun n => Hfun⟩ _).2 Hs h
 #align first_order.language.substructure.closure_induction FirstOrder.Language.Substructure.closure_induction
+-/
 
+#print FirstOrder.Language.Substructure.dense_induction /-
 /-- If `s` is a dense set in a structure `M`, `substructure.closure L s = ⊤`, then in order to prove
 that some predicate `p` holds for all `x : M` it suffices to verify `p x` for `x ∈ s`, and verify
 that `p` is preserved under function symbols. -/
@@ -357,9 +480,16 @@ theorem dense_induction {p : M → Prop} (x : M) {s : Set M} (hs : closure L s =
   have : ∀ x ∈ closure L s, p x := fun x hx => closure_induction hx Hs fun n => Hfun
   simpa [hs] using this x
 #align first_order.language.substructure.dense_induction FirstOrder.Language.Substructure.dense_induction
+-/
 
 variable (L) (M)
 
+/- warning: first_order.language.substructure.gi -> FirstOrder.Language.Substructure.gi is a dubious translation:
+lean 3 declaration is
+  forall (L : FirstOrder.Language.{u1, u2}) (M : Type.{u3}) [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], GaloisInsertion.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))
+but is expected to have type
+  forall (L : FirstOrder.Language.{u1, u2}) (M : Type.{u3}) [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], GaloisInsertion.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1)) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.gi FirstOrder.Language.Substructure.giₓ'. -/
 /-- `closure` forms a Galois insertion with the coercion to set. -/
 protected def gi : GaloisInsertion (@closure L M _) coe
     where
@@ -371,30 +501,58 @@ protected def gi : GaloisInsertion (@closure L M _) coe
 
 variable {L} {M}
 
+#print FirstOrder.Language.Substructure.closure_eq /-
 /-- Closure of a substructure `S` equals `S`. -/
 @[simp]
 theorem closure_eq : closure L (S : Set M) = S :=
   (Substructure.gi L M).l_u_eq S
 #align first_order.language.substructure.closure_eq FirstOrder.Language.Substructure.closure_eq
+-/
 
+/- warning: first_order.language.substructure.closure_empty -> FirstOrder.Language.Substructure.closure_empty is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (EmptyCollection.emptyCollection.{u3} (Set.{u3} M) (Set.hasEmptyc.{u3} M))) (Bot.bot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toHasBot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (EmptyCollection.emptyCollection.{u3} (Set.{u3} M) (Set.instEmptyCollectionSet.{u3} M))) (Bot.bot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toBot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_empty FirstOrder.Language.Substructure.closure_emptyₓ'. -/
 @[simp]
 theorem closure_empty : closure L (∅ : Set M) = ⊥ :=
   (Substructure.gi L M).gc.l_bot
 #align first_order.language.substructure.closure_empty FirstOrder.Language.Substructure.closure_empty
 
+#print FirstOrder.Language.Substructure.closure_univ /-
 @[simp]
 theorem closure_univ : closure L (univ : Set M) = ⊤ :=
   @coe_top L M _ ▸ closure_eq ⊤
 #align first_order.language.substructure.closure_univ FirstOrder.Language.Substructure.closure_univ
+-/
 
+/- warning: first_order.language.substructure.closure_union -> FirstOrder.Language.Substructure.closure_union is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] (s : Set.{u3} M) (t : Set.{u3} M), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.hasUnion.{u3} M) s t)) (Sup.sup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SemilatticeSup.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Lattice.toSemilatticeSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) t))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] (s : Set.{u3} M) (t : Set.{u3} M), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.instUnionSet.{u3} M) s t)) (Sup.sup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SemilatticeSup.toSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Lattice.toSemilatticeSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) t))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_union FirstOrder.Language.Substructure.closure_unionₓ'. -/
 theorem closure_union (s t : Set M) : closure L (s ∪ t) = closure L s ⊔ closure L t :=
   (Substructure.gi L M).gc.l_sup
 #align first_order.language.substructure.closure_union FirstOrder.Language.Substructure.closure_union
 
+/- warning: first_order.language.substructure.closure_Union -> FirstOrder.Language.Substructure.closure_unionᵢ is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {ι : Sort.{u4}} (s : ι -> (Set.{u3} M)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Set.unionᵢ.{u3, u4} M ι (fun (i : ι) => s i))) (supᵢ.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι (fun (i : ι) => coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (s i)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] {ι : Sort.{u1}} (s : ι -> (Set.{u4} M)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) (Set.unionᵢ.{u4, u1} M ι (fun (i : ι) => s i))) (supᵢ.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))) ι (fun (i : ι) => LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) (s i)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_Union FirstOrder.Language.Substructure.closure_unionᵢₓ'. -/
 theorem closure_unionᵢ {ι} (s : ι → Set M) : closure L (⋃ i, s i) = ⨆ i, closure L (s i) :=
   (Substructure.gi L M).gc.l_supᵢ
 #align first_order.language.substructure.closure_Union FirstOrder.Language.Substructure.closure_unionᵢ
 
+/- warning: first_order.language.substructure.small_bot -> FirstOrder.Language.Substructure.small_bot is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], Small.{u1, u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (Bot.bot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toHasBot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M], Small.{u1, u3} (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (Bot.bot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toBot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.small_bot FirstOrder.Language.Substructure.small_botₓ'. -/
 instance small_bot : Small.{u} (⊥ : L.Substructure M) :=
   by
   rw [← closure_empty]
@@ -406,6 +564,7 @@ instance small_bot : Small.{u} (⊥ : L.Substructure M) :=
 -/
 
 
+#print FirstOrder.Language.Substructure.comap /-
 /-- The preimage of a substructure along a homomorphism is a substructure. -/
 @[simps]
 def comap (φ : M →[L] N) (S : L.Substructure N) : L.Substructure M
@@ -415,22 +574,42 @@ def comap (φ : M →[L] N) (S : L.Substructure N) : L.Substructure M
     rw [mem_preimage, φ.map_fun]
     exact S.fun_mem f (φ ∘ x) hx
 #align first_order.language.substructure.comap FirstOrder.Language.Substructure.comap
+-/
 
+/- warning: first_order.language.substructure.mem_comap -> FirstOrder.Language.Substructure.mem_comap is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {x : M}, Iff (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) (Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x) S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {x : M}, Iff (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)) (Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) x) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f x) S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.mem_comap FirstOrder.Language.Substructure.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap {S : L.Substructure N} {f : M →[L] N} {x : M} : x ∈ S.comap f ↔ f x ∈ S :=
   Iff.rfl
 #align first_order.language.substructure.mem_comap FirstOrder.Language.Substructure.mem_comap
 
+/- warning: first_order.language.substructure.comap_comap -> FirstOrder.Language.Substructure.comap_comap is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (S : FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u4, u5} L N P _inst_2 _inst_3 g S)) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u5} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f) S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u1} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u2} L P] (S : FirstOrder.Language.Substructure.{u3, u4, u2} L P _inst_3) (g : FirstOrder.Language.Hom.{u3, u4, u1, u2} L N P _inst_2 _inst_3) (f : FirstOrder.Language.Hom.{u3, u4, u5, u1} L M N _inst_1 _inst_2), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u3, u4, u1, u2} L N P _inst_2 _inst_3 g S)) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u3, u4, u5, u1, u2} L M N _inst_1 _inst_2 P _inst_3 g f) S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_comap FirstOrder.Language.Substructure.comap_comapₓ'. -/
 theorem comap_comap (S : L.Substructure P) (g : N →[L] P) (f : M →[L] N) :
     (S.comap g).comap f = S.comap (g.comp f) :=
   rfl
 #align first_order.language.substructure.comap_comap FirstOrder.Language.Substructure.comap_comap
 
+/- warning: first_order.language.substructure.comap_id -> FirstOrder.Language.Substructure.comap_id is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {P : Type.{u3}} [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u3} L P] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L P _inst_3), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L P _inst_3) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u3} L P P _inst_3 _inst_3 (FirstOrder.Language.Hom.id.{u1, u2, u3} L P _inst_3) S) S
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {P : Type.{u1}} [_inst_3 : FirstOrder.Language.Structure.{u2, u3, u1} L P] (S : FirstOrder.Language.Substructure.{u2, u3, u1} L P _inst_3), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L P _inst_3) (FirstOrder.Language.Substructure.comap.{u2, u3, u1, u1} L P P _inst_3 _inst_3 (FirstOrder.Language.Hom.id.{u2, u3, u1} L P _inst_3) S) S
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_id FirstOrder.Language.Substructure.comap_idₓ'. -/
 @[simp]
 theorem comap_id (S : L.Substructure P) : S.comap (Hom.id _ _) = S :=
   ext (by simp)
 #align first_order.language.substructure.comap_id FirstOrder.Language.Substructure.comap_id
 
+#print FirstOrder.Language.Substructure.map /-
 /-- The image of a substructure along a homomorphism is a substructure. -/
 @[simps]
 def map (φ : M →[L] N) (S : L.Substructure M) : L.Substructure N
@@ -444,108 +623,243 @@ def map (φ : M →[L] N) (S : L.Substructure M) : L.Substructure N
         simp only [hom.map_fun, SetLike.mem_coe]
         exact congr rfl (funext fun i => (Classical.choose_spec (hx i)).2)⟩
 #align first_order.language.substructure.map FirstOrder.Language.Substructure.map
+-/
 
+/- warning: first_order.language.substructure.mem_map -> FirstOrder.Language.Substructure.mem_map is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {y : N}, Iff (Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) y (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) (Exists.{succ u3} M (fun (x : M) => Exists.{0} (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S) (fun (H : Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S) => Eq.{succ u4} N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x) y)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {y : N}, Iff (Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) y (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)) (Exists.{succ u4} M (fun (x : M) => And (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x S) (Eq.{succ u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (a : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) a) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f x) y)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.mem_map FirstOrder.Language.Substructure.mem_mapₓ'. -/
 @[simp]
 theorem mem_map {f : M →[L] N} {S : L.Substructure M} {y : N} : y ∈ S.map f ↔ ∃ x ∈ S, f x = y :=
   mem_image_iff_bex
 #align first_order.language.substructure.mem_map FirstOrder.Language.Substructure.mem_map
 
+/- warning: first_order.language.substructure.mem_map_of_mem -> FirstOrder.Language.Substructure.mem_map_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {x : M}, (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S) -> (Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {x : M}, (Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x S) -> (Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) x) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f x) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.mem_map_of_mem FirstOrder.Language.Substructure.mem_map_of_memₓ'. -/
 theorem mem_map_of_mem (f : M →[L] N) {S : L.Substructure M} {x : M} (hx : x ∈ S) : f x ∈ S.map f :=
   mem_image_of_mem f hx
 #align first_order.language.substructure.mem_map_of_mem FirstOrder.Language.Substructure.mem_map_of_mem
 
+/- warning: first_order.language.substructure.apply_coe_mem_map -> FirstOrder.Language.Substructure.apply_coe_mem_map is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x : coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S), Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) M (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) M (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) M (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) M (coeSubtype.{succ u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S))))) x)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (x : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x S)), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) (Subtype.val.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Set.{u4} M) (Set.instMembershipSet.{u4} M) x (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) S)) x)) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f (Subtype.val.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Set.{u4} M) (Set.instMembershipSet.{u4} M) x (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) S)) x)) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.apply_coe_mem_map FirstOrder.Language.Substructure.apply_coe_mem_mapₓ'. -/
 theorem apply_coe_mem_map (f : M →[L] N) (S : L.Substructure M) (x : S) : f x ∈ S.map f :=
   mem_map_of_mem f x.Prop
 #align first_order.language.substructure.apply_coe_mem_map FirstOrder.Language.Substructure.apply_coe_mem_map
 
+/- warning: first_order.language.substructure.map_map -> FirstOrder.Language.Substructure.map_map is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (FirstOrder.Language.Substructure.map.{u1, u2, u4, u5} L N P _inst_2 _inst_3 g (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u5} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f) S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} {P : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u1} L P] (S : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (g : FirstOrder.Language.Hom.{u3, u4, u2, u1} L N P _inst_2 _inst_3) (f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (FirstOrder.Language.Substructure.map.{u3, u4, u2, u1} L N P _inst_2 _inst_3 g (FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f S)) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u1} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 P _inst_3 g f) S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_map FirstOrder.Language.Substructure.map_mapₓ'. -/
 theorem map_map (g : N →[L] P) (f : M →[L] N) : (S.map f).map g = S.map (g.comp f) :=
   SetLike.coe_injective <| image_image _ _ _
 #align first_order.language.substructure.map_map FirstOrder.Language.Substructure.map_map
 
+/- warning: first_order.language.substructure.map_le_iff_le_comap -> FirstOrder.Language.Substructure.map_le_iff_le_comap is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2}, Iff (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) T) (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_le_iff_le_comap FirstOrder.Language.Substructure.map_le_iff_le_comapₓ'. -/
 theorem map_le_iff_le_comap {f : M →[L] N} {S : L.Substructure M} {T : L.Substructure N} :
     S.map f ≤ T ↔ S ≤ T.comap f :=
   image_subset_iff
 #align first_order.language.substructure.map_le_iff_le_comap FirstOrder.Language.Substructure.map_le_iff_le_comap
 
+/- warning: first_order.language.substructure.gc_map_comap -> FirstOrder.Language.Substructure.gc_map_comap is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), GaloisConnection.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), GaloisConnection.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.gc_map_comap FirstOrder.Language.Substructure.gc_map_comapₓ'. -/
 theorem gc_map_comap (f : M →[L] N) : GaloisConnection (map f) (comap f) := fun S T =>
   map_le_iff_le_comap
 #align first_order.language.substructure.gc_map_comap FirstOrder.Language.Substructure.gc_map_comap
 
+/- warning: first_order.language.substructure.map_le_of_le_comap -> FirstOrder.Language.Substructure.map_le_of_le_comap is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) -> (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T)) -> (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) T)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_le_of_le_comap FirstOrder.Language.Substructure.map_le_of_le_comapₓ'. -/
 theorem map_le_of_le_comap {T : L.Substructure N} {f : M →[L] N} : S ≤ T.comap f → S.map f ≤ T :=
   (gc_map_comap f).l_le
 #align first_order.language.substructure.map_le_of_le_comap FirstOrder.Language.Substructure.map_le_of_le_comap
 
+/- warning: first_order.language.substructure.le_comap_of_map_le -> FirstOrder.Language.Substructure.le_comap_of_map_le is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) T) -> (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) T) -> (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.le_comap_of_map_le FirstOrder.Language.Substructure.le_comap_of_map_leₓ'. -/
 theorem le_comap_of_map_le {T : L.Substructure N} {f : M →[L] N} : S.map f ≤ T → S ≤ T.comap f :=
   (gc_map_comap f).le_u
 #align first_order.language.substructure.le_comap_of_map_le FirstOrder.Language.Substructure.le_comap_of_map_le
 
+/- warning: first_order.language.substructure.le_comap_map -> FirstOrder.Language.Substructure.le_comap_map is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.le_comap_map FirstOrder.Language.Substructure.le_comap_mapₓ'. -/
 theorem le_comap_map {f : M →[L] N} : S ≤ (S.map f).comap f :=
   (gc_map_comap f).le_u_l _
 #align first_order.language.substructure.le_comap_map FirstOrder.Language.Substructure.le_comap_map
 
+/- warning: first_order.language.substructure.map_comap_le -> FirstOrder.Language.Substructure.map_comap_le is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) S
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)) S
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_comap_le FirstOrder.Language.Substructure.map_comap_leₓ'. -/
 theorem map_comap_le {S : L.Substructure N} {f : M →[L] N} : (S.comap f).map f ≤ S :=
   (gc_map_comap f).l_u_le _
 #align first_order.language.substructure.map_comap_le FirstOrder.Language.Substructure.map_comap_le
 
+/- warning: first_order.language.substructure.monotone_map -> FirstOrder.Language.Substructure.monotone_map is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, Monotone.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, Monotone.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.monotone_map FirstOrder.Language.Substructure.monotone_mapₓ'. -/
 theorem monotone_map {f : M →[L] N} : Monotone (map f) :=
   (gc_map_comap f).monotone_l
 #align first_order.language.substructure.monotone_map FirstOrder.Language.Substructure.monotone_map
 
+/- warning: first_order.language.substructure.monotone_comap -> FirstOrder.Language.Substructure.monotone_comap is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, Monotone.{u4, u3} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, Monotone.{u1, u4} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.monotone_comap FirstOrder.Language.Substructure.monotone_comapₓ'. -/
 theorem monotone_comap {f : M →[L] N} : Monotone (comap f) :=
   (gc_map_comap f).monotone_u
 #align first_order.language.substructure.monotone_comap FirstOrder.Language.Substructure.monotone_comap
 
+/- warning: first_order.language.substructure.map_comap_map -> FirstOrder.Language.Substructure.map_comap_map is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_comap_map FirstOrder.Language.Substructure.map_comap_mapₓ'. -/
 @[simp]
 theorem map_comap_map {f : M →[L] N} : ((S.map f).comap f).map f = S.map f :=
   (gc_map_comap f).l_u_l_eq_l _
 #align first_order.language.substructure.map_comap_map FirstOrder.Language.Substructure.map_comap_map
 
+/- warning: first_order.language.substructure.comap_map_comap -> FirstOrder.Language.Substructure.comap_map_comap is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S))) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_map_comap FirstOrder.Language.Substructure.comap_map_comapₓ'. -/
 @[simp]
 theorem comap_map_comap {S : L.Substructure N} {f : M →[L] N} :
     ((S.comap f).map f).comap f = S.comap f :=
   (gc_map_comap f).u_l_u_eq_u _
 #align first_order.language.substructure.comap_map_comap FirstOrder.Language.Substructure.comap_map_comap
 
+/- warning: first_order.language.substructure.map_sup -> FirstOrder.Language.Substructure.map_sup is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Sup.sup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SemilatticeSup.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Lattice.toSemilatticeSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S T)) (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SemilatticeSup.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (T : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SemilatticeSup.toSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S T)) (Sup.sup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SemilatticeSup.toSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Lattice.toSemilatticeSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_sup FirstOrder.Language.Substructure.map_supₓ'. -/
 theorem map_sup (S T : L.Substructure M) (f : M →[L] N) : (S ⊔ T).map f = S.map f ⊔ T.map f :=
   (gc_map_comap f).l_sup
 #align first_order.language.substructure.map_sup FirstOrder.Language.Substructure.map_sup
 
+/- warning: first_order.language.substructure.map_supr -> FirstOrder.Language.Substructure.map_supᵢ is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Sort.{u5}} (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (supᵢ.{u3, u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι s)) (supᵢ.{u4, u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (s i)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u1} L N] {ι : Sort.{u2}} (f : FirstOrder.Language.Hom.{u3, u4, u5, u1} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (supᵢ.{u5, u2} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι s)) (supᵢ.{u1, u2} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u1} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (s i)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_supᵢₓ'. -/
 theorem map_supᵢ {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure M) :
     (supᵢ s).map f = ⨆ i, (s i).map f :=
   (gc_map_comap f).l_supᵢ
 #align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_supᵢ
 
+/- warning: first_order.language.substructure.comap_inf -> FirstOrder.Language.Substructure.comap_inf is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u1, u2, u4} L N _inst_2) S T)) (Inf.inf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Inf.inf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u2, u3, u1} L N _inst_2) S T)) (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_inf FirstOrder.Language.Substructure.comap_infₓ'. -/
 theorem comap_inf (S T : L.Substructure N) (f : M →[L] N) :
     (S ⊓ T).comap f = S.comap f ⊓ T.comap f :=
   (gc_map_comap f).u_inf
 #align first_order.language.substructure.comap_inf FirstOrder.Language.Substructure.comap_inf
 
+/- warning: first_order.language.substructure.comap_infi -> FirstOrder.Language.Substructure.comap_infᵢ is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Sort.{u5}} (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (infᵢ.{u4, u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι s)) (infᵢ.{u3, u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (s i)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u1} L N] {ι : Sort.{u2}} (f : FirstOrder.Language.Hom.{u3, u4, u5, u1} L M N _inst_1 _inst_2) (s : ι -> (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (infᵢ.{u1, u2} (FirstOrder.Language.Substructure.{u3, u4, u1} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u1} L N _inst_2) ι s)) (infᵢ.{u5, u2} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u1} L M N _inst_1 _inst_2 f (s i)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_infᵢₓ'. -/
 theorem comap_infᵢ {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure N) :
     (infᵢ s).comap f = ⨅ i, (s i).comap f :=
   (gc_map_comap f).u_infᵢ
 #align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_infᵢ
 
+/- warning: first_order.language.substructure.map_bot -> FirstOrder.Language.Substructure.map_bot is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Bot.bot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toHasBot.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (Bot.bot.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toHasBot.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Bot.bot.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toBot.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (Bot.bot.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toBot.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_bot FirstOrder.Language.Substructure.map_botₓ'. -/
 @[simp]
 theorem map_bot (f : M →[L] N) : (⊥ : L.Substructure M).map f = ⊥ :=
   (gc_map_comap f).l_bot
 #align first_order.language.substructure.map_bot FirstOrder.Language.Substructure.map_bot
 
+/- warning: first_order.language.substructure.comap_top -> FirstOrder.Language.Substructure.comap_top is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Top.top.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u1, u2, u4} L N _inst_2))) (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Top.top.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u2, u3, u1} L N _inst_2))) (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_top FirstOrder.Language.Substructure.comap_topₓ'. -/
 @[simp]
 theorem comap_top (f : M →[L] N) : (⊤ : L.Substructure N).comap f = ⊤ :=
   (gc_map_comap f).u_top
 #align first_order.language.substructure.comap_top FirstOrder.Language.Substructure.comap_top
 
+#print FirstOrder.Language.Substructure.map_id /-
 @[simp]
 theorem map_id (S : L.Substructure M) : S.map (Hom.id L M) = S :=
   ext fun x => ⟨fun ⟨_, h, rfl⟩ => h, fun h => ⟨_, h, rfl⟩⟩
 #align first_order.language.substructure.map_id FirstOrder.Language.Substructure.map_id
+-/
 
+/- warning: first_order.language.substructure.map_closure -> FirstOrder.Language.Substructure.map_closure is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (s : Set.{u3} M), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)) (coeFn.{succ u4, succ u4} (LowerAdjoint.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) (fun (_x : LowerAdjoint.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) => (Set.{u4} N) -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)) (LowerAdjoint.hasCoeToFun.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u4} L N _inst_2) (Set.image.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) s))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (s : Set.{u4} M), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) s)) (LowerAdjoint.toFun.{u1, u1} (Set.{u1} N) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (Set.{u1} N) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} N) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} N) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} N) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} N) (Set.instCompleteBooleanAlgebraSet.{u1} N))))))) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FirstOrder.Language.Substructure.closure.{u2, u3, u1} L N _inst_2) (Set.image.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) s))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_closure FirstOrder.Language.Substructure.map_closureₓ'. -/
 theorem map_closure (f : M →[L] N) (s : Set M) : (closure L s).map f = closure L (f '' s) :=
   Eq.symm <|
     closure_eq_of_le (Set.image_subset f subset_closure) <|
       map_le_iff_le_comap.2 <| closure_le.2 fun x hx => subset_closure ⟨x, hx, rfl⟩
 #align first_order.language.substructure.map_closure FirstOrder.Language.Substructure.map_closure
 
+/- warning: first_order.language.substructure.closure_image -> FirstOrder.Language.Substructure.closure_image is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {s : Set.{u3} M} (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (coeFn.{succ u4, succ u4} (LowerAdjoint.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) (fun (_x : LowerAdjoint.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) => (Set.{u4} N) -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)) (LowerAdjoint.hasCoeToFun.{u4, u4} (Set.{u4} N) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (Set.{u4} N) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} N) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} N) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} N) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} N) (Set.completeBooleanAlgebra.{u4} N))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u4} L N _inst_2) (Set.image.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) s)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {s : Set.{u4} M} (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (LowerAdjoint.toFun.{u1, u1} (Set.{u1} N) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (Set.{u1} N) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} N) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} N) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} N) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} N) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} N) (Set.instCompleteBooleanAlgebraSet.{u1} N))))))) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FirstOrder.Language.Substructure.closure.{u2, u3, u1} L N _inst_2) (Set.image.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) s)) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_image FirstOrder.Language.Substructure.closure_imageₓ'. -/
 @[simp]
 theorem closure_image (f : M →[L] N) : closure L (f '' s) = map f (closure L s) :=
   (map_closure f s).symm
@@ -557,45 +871,105 @@ variable {ι : Type _} {f : M →[L] N} (hf : Function.Injective f)
 
 include hf
 
+/- warning: first_order.language.substructure.gci_map_comap -> FirstOrder.Language.Substructure.gciMapComap is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (GaloisCoinsertion.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (GaloisCoinsertion.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.gci_map_comap FirstOrder.Language.Substructure.gciMapComapₓ'. -/
 /-- `map f` and `comap f` form a `galois_coinsertion` when `f` is injective. -/
 def gciMapComap : GaloisCoinsertion (map f) (comap f) :=
   (gc_map_comap f).toGaloisCoinsertion fun S x => by simp [mem_comap, mem_map, hf.eq_iff]
 #align first_order.language.substructure.gci_map_comap FirstOrder.Language.Substructure.gciMapComap
 
+/- warning: first_order.language.substructure.comap_map_eq_of_injective -> FirstOrder.Language.Substructure.comap_map_eq_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)) S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_map_eq_of_injective FirstOrder.Language.Substructure.comap_map_eq_of_injectiveₓ'. -/
 theorem comap_map_eq_of_injective (S : L.Substructure M) : (S.map f).comap f = S :=
   (gciMapComap hf).u_l_eq _
 #align first_order.language.substructure.comap_map_eq_of_injective FirstOrder.Language.Substructure.comap_map_eq_of_injective
 
+/- warning: first_order.language.substructure.comap_surjective_of_injective -> FirstOrder.Language.Substructure.comap_surjective_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (Function.Surjective.{succ u4, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (Function.Surjective.{succ u1, succ u4} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_surjective_of_injective FirstOrder.Language.Substructure.comap_surjective_of_injectiveₓ'. -/
 theorem comap_surjective_of_injective : Function.Surjective (comap f) :=
   (gciMapComap hf).u_surjective
 #align first_order.language.substructure.comap_surjective_of_injective FirstOrder.Language.Substructure.comap_surjective_of_injective
 
+/- warning: first_order.language.substructure.map_injective_of_injective -> FirstOrder.Language.Substructure.map_injective_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (Function.Injective.{succ u3, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (Function.Injective.{succ u4, succ u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_injective_of_injective FirstOrder.Language.Substructure.map_injective_of_injectiveₓ'. -/
 theorem map_injective_of_injective : Function.Injective (map f) :=
   (gciMapComap hf).l_injective
 #align first_order.language.substructure.map_injective_of_injective FirstOrder.Language.Substructure.map_injective_of_injective
 
+/- warning: first_order.language.substructure.comap_inf_map_of_injective -> FirstOrder.Language.Substructure.comap_inf_map_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))) (Inf.inf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u1, u2, u3} L M _inst_1) S T))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (T : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Inf.inf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))) (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u2, u3, u4} L M _inst_1) S T))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_inf_map_of_injective FirstOrder.Language.Substructure.comap_inf_map_of_injectiveₓ'. -/
 theorem comap_inf_map_of_injective (S T : L.Substructure M) : (S.map f ⊓ T.map f).comap f = S ⊓ T :=
   (gciMapComap hf).u_inf_l _ _
 #align first_order.language.substructure.comap_inf_map_of_injective FirstOrder.Language.Substructure.comap_inf_map_of_injective
 
+/- warning: first_order.language.substructure.comap_infi_map_of_injective -> FirstOrder.Language.Substructure.comap_infᵢ_map_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (infᵢ.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (infᵢ.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι S))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Injective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (infᵢ.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u2} L N _inst_2) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (infᵢ.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι S))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_infi_map_of_injective FirstOrder.Language.Substructure.comap_infᵢ_map_of_injectiveₓ'. -/
 theorem comap_infᵢ_map_of_injective (S : ι → L.Substructure M) :
     (⨅ i, (S i).map f).comap f = infᵢ S :=
   (gciMapComap hf).u_infᵢ_l _
 #align first_order.language.substructure.comap_infi_map_of_injective FirstOrder.Language.Substructure.comap_infᵢ_map_of_injective
 
+/- warning: first_order.language.substructure.comap_sup_map_of_injective -> FirstOrder.Language.Substructure.comap_sup_map_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SemilatticeSup.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))) (Sup.sup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SemilatticeSup.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Lattice.toSemilatticeSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S T))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (T : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1), Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Sup.sup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SemilatticeSup.toSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Lattice.toSemilatticeSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))) (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SemilatticeSup.toSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S T))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_sup_map_of_injective FirstOrder.Language.Substructure.comap_sup_map_of_injectiveₓ'. -/
 theorem comap_sup_map_of_injective (S T : L.Substructure M) : (S.map f ⊔ T.map f).comap f = S ⊔ T :=
   (gciMapComap hf).u_sup_l _ _
 #align first_order.language.substructure.comap_sup_map_of_injective FirstOrder.Language.Substructure.comap_sup_map_of_injective
 
+/- warning: first_order.language.substructure.comap_supr_map_of_injective -> FirstOrder.Language.Substructure.comap_supᵢ_map_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (supᵢ.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (supᵢ.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι S))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Injective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1)), Eq.{succ u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (supᵢ.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u2} L N _inst_2))) ι (fun (i : ι) => FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (supᵢ.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι S))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_supr_map_of_injective FirstOrder.Language.Substructure.comap_supᵢ_map_of_injectiveₓ'. -/
 theorem comap_supᵢ_map_of_injective (S : ι → L.Substructure M) :
     (⨆ i, (S i).map f).comap f = supᵢ S :=
   (gciMapComap hf).u_supᵢ_l _
 #align first_order.language.substructure.comap_supr_map_of_injective FirstOrder.Language.Substructure.comap_supᵢ_map_of_injective
 
+/- warning: first_order.language.substructure.map_le_map_iff_of_injective -> FirstOrder.Language.Substructure.map_le_map_iff_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1} {T : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1}, Iff (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T)) (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) S T))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_le_map_iff_of_injective FirstOrder.Language.Substructure.map_le_map_iff_of_injectiveₓ'. -/
 theorem map_le_map_iff_of_injective {S T : L.Substructure M} : S.map f ≤ T.map f ↔ S ≤ T :=
   (gciMapComap hf).l_le_l_iff
 #align first_order.language.substructure.map_le_map_iff_of_injective FirstOrder.Language.Substructure.map_le_map_iff_of_injective
 
+/- warning: first_order.language.substructure.map_strict_mono_of_injective -> FirstOrder.Language.Substructure.map_strictMono_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (StrictMono.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Injective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (StrictMono.{u4, u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_strict_mono_of_injective FirstOrder.Language.Substructure.map_strictMono_of_injectiveₓ'. -/
 theorem map_strictMono_of_injective : StrictMono (map f) :=
   (gciMapComap hf).strictMono_l
 #align first_order.language.substructure.map_strict_mono_of_injective FirstOrder.Language.Substructure.map_strictMono_of_injective
@@ -608,6 +982,12 @@ variable {ι : Type _} {f : M →[L] N} (hf : Function.Surjective f)
 
 include hf
 
+/- warning: first_order.language.substructure.gi_map_comap -> FirstOrder.Language.Substructure.giMapComap is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (GaloisInsertion.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (GaloisInsertion.{u3, u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.gi_map_comap FirstOrder.Language.Substructure.giMapComapₓ'. -/
 /-- `map f` and `comap f` form a `galois_insertion` when `f` is surjective. -/
 def giMapComap : GaloisInsertion (map f) (comap f) :=
   (gc_map_comap f).toGaloisInsertion fun S x h =>
@@ -615,66 +995,127 @@ def giMapComap : GaloisInsertion (map f) (comap f) :=
     mem_map.2 ⟨y, by simp [hy, h]⟩
 #align first_order.language.substructure.gi_map_comap FirstOrder.Language.Substructure.giMapComap
 
+/- warning: first_order.language.substructure.map_comap_eq_of_surjective -> FirstOrder.Language.Substructure.map_comap_eq_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S)) S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S)) S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_comap_eq_of_surjective FirstOrder.Language.Substructure.map_comap_eq_of_surjectiveₓ'. -/
 theorem map_comap_eq_of_surjective (S : L.Substructure N) : (S.comap f).map f = S :=
   (giMapComap hf).l_u_eq _
 #align first_order.language.substructure.map_comap_eq_of_surjective FirstOrder.Language.Substructure.map_comap_eq_of_surjective
 
+/- warning: first_order.language.substructure.map_surjective_of_surjective -> FirstOrder.Language.Substructure.map_surjective_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (Function.Surjective.{succ u3, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (Function.Surjective.{succ u4, succ u1} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_surjective_of_surjective FirstOrder.Language.Substructure.map_surjective_of_surjectiveₓ'. -/
 theorem map_surjective_of_surjective : Function.Surjective (map f) :=
   (giMapComap hf).l_surjective
 #align first_order.language.substructure.map_surjective_of_surjective FirstOrder.Language.Substructure.map_surjective_of_surjective
 
+/- warning: first_order.language.substructure.comap_injective_of_surjective -> FirstOrder.Language.Substructure.comap_injective_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (Function.Injective.{succ u4, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (Function.Injective.{succ u1, succ u4} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_injective_of_surjective FirstOrder.Language.Substructure.comap_injective_of_surjectiveₓ'. -/
 theorem comap_injective_of_surjective : Function.Injective (comap f) :=
   (giMapComap hf).u_injective
 #align first_order.language.substructure.comap_injective_of_surjective FirstOrder.Language.Substructure.comap_injective_of_surjective
 
+/- warning: first_order.language.substructure.map_inf_comap_of_surjective -> FirstOrder.Language.Substructure.map_inf_comap_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Inf.inf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))) (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u1, u2, u4} L N _inst_2) S T))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Inf.inf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instInf.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))) (Inf.inf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instInf.{u2, u3, u1} L N _inst_2) S T))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_inf_comap_of_surjective FirstOrder.Language.Substructure.map_inf_comap_of_surjectiveₓ'. -/
 theorem map_inf_comap_of_surjective (S T : L.Substructure N) :
     (S.comap f ⊓ T.comap f).map f = S ⊓ T :=
   (giMapComap hf).l_inf_u _ _
 #align first_order.language.substructure.map_inf_comap_of_surjective FirstOrder.Language.Substructure.map_inf_comap_of_surjective
 
+/- warning: first_order.language.substructure.map_infi_comap_of_surjective -> FirstOrder.Language.Substructure.map_infᵢ_comap_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (infᵢ.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u3} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (infᵢ.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u1, u2, u4} L N _inst_2) ι S))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2)), Eq.{succ u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (infᵢ.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u5} L M _inst_1) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (infᵢ.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instInfSet.{u3, u4, u2} L N _inst_2) ι S))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_infi_comap_of_surjective FirstOrder.Language.Substructure.map_infᵢ_comap_of_surjectiveₓ'. -/
 theorem map_infᵢ_comap_of_surjective (S : ι → L.Substructure N) :
     (⨅ i, (S i).comap f).map f = infᵢ S :=
   (giMapComap hf).l_infᵢ_u _
 #align first_order.language.substructure.map_infi_comap_of_surjective FirstOrder.Language.Substructure.map_infᵢ_comap_of_surjective
 
+/- warning: first_order.language.substructure.map_sup_comap_of_surjective -> FirstOrder.Language.Substructure.map_sup_comap_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Sup.sup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SemilatticeSup.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Lattice.toSemilatticeSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T))) (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SemilatticeSup.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))))) S T))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall (S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Sup.sup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SemilatticeSup.toSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Lattice.toSemilatticeSup.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (ConditionallyCompleteLattice.toLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T))) (Sup.sup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SemilatticeSup.toSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Lattice.toSemilatticeSup.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (ConditionallyCompleteLattice.toLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) S T))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_sup_comap_of_surjective FirstOrder.Language.Substructure.map_sup_comap_of_surjectiveₓ'. -/
 theorem map_sup_comap_of_surjective (S T : L.Substructure N) :
     (S.comap f ⊔ T.comap f).map f = S ⊔ T :=
   (giMapComap hf).l_sup_u _ _
 #align first_order.language.substructure.map_sup_comap_of_surjective FirstOrder.Language.Substructure.map_sup_comap_of_surjective
 
+/- warning: first_order.language.substructure.map_supr_comap_of_surjective -> FirstOrder.Language.Substructure.map_supᵢ_comap_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {ι : Type.{u5}} {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2)), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (supᵢ.{u3, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (ConditionallyCompleteLattice.toHasSup.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (S i)))) (supᵢ.{u4, succ u5} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (ConditionallyCompleteLattice.toHasSup.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u4} L N _inst_2))) ι S))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] {ι : Type.{u1}} {f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u5, succ u2} M N (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f)) -> (forall (S : ι -> (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2)), Eq.{succ u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.map.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (supᵢ.{u5, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (ConditionallyCompleteLattice.toSupSet.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))) ι (fun (i : ι) => FirstOrder.Language.Substructure.comap.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f (S i)))) (supᵢ.{u2, succ u1} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (ConditionallyCompleteLattice.toSupSet.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (CompleteLattice.toConditionallyCompleteLattice.{u2} (FirstOrder.Language.Substructure.{u3, u4, u2} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u2} L N _inst_2))) ι S))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.map_supr_comap_of_surjective FirstOrder.Language.Substructure.map_supᵢ_comap_of_surjectiveₓ'. -/
 theorem map_supᵢ_comap_of_surjective (S : ι → L.Substructure N) :
     (⨆ i, (S i).comap f).map f = supᵢ S :=
   (giMapComap hf).l_supᵢ_u _
 #align first_order.language.substructure.map_supr_comap_of_surjective FirstOrder.Language.Substructure.map_supᵢ_comap_of_surjective
 
+/- warning: first_order.language.substructure.comap_le_comap_iff_of_surjective -> FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2} {T : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f T)) (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) S T))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (forall {S : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2} {T : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1))))) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f S) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f T)) (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) S T))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_le_comap_iff_of_surjective FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjectiveₓ'. -/
 theorem comap_le_comap_iff_of_surjective {S T : L.Substructure N} : S.comap f ≤ T.comap f ↔ S ≤ T :=
   (giMapComap hf).u_le_u_iff
 #align first_order.language.substructure.comap_le_comap_iff_of_surjective FirstOrder.Language.Substructure.comap_le_comap_iff_of_surjective
 
+/- warning: first_order.language.substructure.comap_strict_mono_of_surjective -> FirstOrder.Language.Substructure.comap_strictMono_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f)) -> (StrictMono.{u4, u3} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f)) -> (StrictMono.{u1, u4} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2)))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.comap_strict_mono_of_surjective FirstOrder.Language.Substructure.comap_strictMono_of_surjectiveₓ'. -/
 theorem comap_strictMono_of_surjective : StrictMono (comap f) :=
   (giMapComap hf).strictMono_u
 #align first_order.language.substructure.comap_strict_mono_of_surjective FirstOrder.Language.Substructure.comap_strictMono_of_surjective
 
 end GaloisInsertion
 
+#print FirstOrder.Language.Substructure.inducedStructure /-
 instance inducedStructure {S : L.Substructure M} : L.Structure S
     where
   funMap n f x := ⟨funMap f fun i => x i, S.fun_mem f (fun i => x i) fun i => (x i).2⟩
   rel_map n r x := RelMap r fun i => (x i : M)
 #align first_order.language.substructure.induced_Structure FirstOrder.Language.Substructure.inducedStructure
+-/
 
+#print FirstOrder.Language.Substructure.subtype /-
 /-- The natural embedding of an `L.substructure` of `M` into `M`. -/
 def subtype (S : L.Substructure M) : S ↪[L] M
     where
   toFun := coe
   inj' := Subtype.coe_injective
 #align first_order.language.substructure.subtype FirstOrder.Language.Substructure.subtype
+-/
 
+#print FirstOrder.Language.Substructure.coeSubtype /-
 @[simp]
 theorem coeSubtype : ⇑S.Subtype = coe :=
   rfl
 #align first_order.language.substructure.coe_subtype FirstOrder.Language.Substructure.coeSubtype
+-/
 
+#print FirstOrder.Language.Substructure.topEquiv /-
 /-- The equivalence between the maximal substructure of a structure and the structure itself. -/
 def topEquiv : (⊤ : L.Substructure M) ≃[L] M
     where
@@ -683,12 +1124,16 @@ def topEquiv : (⊤ : L.Substructure M) ≃[L] M
   left_inv m := by simp
   right_inv m := rfl
 #align first_order.language.substructure.top_equiv FirstOrder.Language.Substructure.topEquiv
+-/
 
+#print FirstOrder.Language.Substructure.coe_topEquiv /-
 @[simp]
 theorem coe_topEquiv : ⇑(topEquiv : (⊤ : L.Substructure M) ≃[L] M) = coe :=
   rfl
 #align first_order.language.substructure.coe_top_equiv FirstOrder.Language.Substructure.coe_topEquiv
+-/
 
+#print FirstOrder.Language.Substructure.closure_induction' /-
 /-- A dependent version of `substructure.closure_induction`. -/
 @[elab_as_elim]
 theorem closure_induction' (s : Set M) {p : ∀ x, x ∈ closure L s → Prop}
@@ -699,6 +1144,7 @@ theorem closure_induction' (s : Set M) {p : ∀ x, x ∈ closure L s → Prop}
   refine' Exists.elim _ fun (hx : x ∈ closure L s) (hc : p x hx) => hc
   exact closure_induction hx (fun x hx => ⟨subset_closure hx, Hs x hx⟩) @Hfun
 #align first_order.language.substructure.closure_induction' FirstOrder.Language.Substructure.closure_induction'
+-/
 
 end Substructure
 
@@ -710,6 +1156,12 @@ variable {L' : Language} [L'.Structure M] (φ : L →ᴸ L') [φ.IsExpansionOn M
 
 include φ
 
+/- warning: first_order.language.Lhom.substructure_reduct -> FirstOrder.Language.LHom.substructureReduct is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4], OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4], OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u4, u5, u3} L' M _inst_4))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.substructure_reduct FirstOrder.Language.LHom.substructureReductₓ'. -/
 /-- Reduces the language of a substructure along a language hom. -/
 def substructureReduct : L'.Substructure M ↪o L.Substructure M
     where
@@ -726,12 +1178,24 @@ def substructureReduct : L'.Substructure M ↪o L.Substructure M
   map_rel_iff' S T := Iff.rfl
 #align first_order.language.Lhom.substructure_reduct FirstOrder.Language.LHom.substructureReduct
 
+/- warning: first_order.language.Lhom.mem_substructure_reduct -> FirstOrder.Language.LHom.mem_substructureReduct is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4] {x : M} {S : FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4}, Iff (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, u4, u5} L M _inst_1 L' _inst_4 φ _inst_5) S)) (Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)) x S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] {L' : FirstOrder.Language.{u2, u1}} [_inst_4 : FirstOrder.Language.Structure.{u2, u1, u5} L' M] (φ : FirstOrder.Language.LHom.{u3, u4, u2, u1} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u3, u4, u2, u1, u5} L L' φ M _inst_1 _inst_4] {x : M} {S : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4}, Iff (Membership.mem.{u5, u5} M ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) (SetLike.instMembership.{u5, u5} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) M (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u5} L M _inst_1)) x (FunLike.coe.{succ u5, succ u5, succ u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (fun (_x : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) _x) (RelHomClass.toFunLike.{u5, u5, u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (FirstOrder.Language.LHom.substructureReduct.{u3, u4, u5, u2, u1} L M _inst_1 L' _inst_4 φ _inst_5) S)) (Membership.mem.{u5, u5} M (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (SetLike.instMembership.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u2, u1, u5} L' M _inst_4)) x S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.mem_substructure_reduct FirstOrder.Language.LHom.mem_substructureReductₓ'. -/
 @[simp]
 theorem mem_substructureReduct {x : M} {S : L'.Substructure M} :
     x ∈ φ.substructureReduct S ↔ x ∈ S :=
   Iff.rfl
 #align first_order.language.Lhom.mem_substructure_reduct FirstOrder.Language.LHom.mem_substructureReduct
 
+/- warning: first_order.language.Lhom.coe_substructure_reduct -> FirstOrder.Language.LHom.coe_substructureReduct is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {L' : FirstOrder.Language.{u4, u5}} [_inst_4 : FirstOrder.Language.Structure.{u4, u5, u3} L' M] (φ : FirstOrder.Language.LHom.{u1, u2, u4, u5} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u1, u2, u4, u5, u3} L L' φ M _inst_1 _inst_4] {S : FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4}, Eq.{succ u3} (Set.{u3} M) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, u4, u5} L M _inst_1 L' _inst_4 φ _inst_5) S)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u4, u5, u3} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u4, u5, u3} L' M _inst_4)))) S)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] {L' : FirstOrder.Language.{u2, u1}} [_inst_4 : FirstOrder.Language.Structure.{u2, u1, u5} L' M] (φ : FirstOrder.Language.LHom.{u3, u4, u2, u1} L L') [_inst_5 : FirstOrder.Language.LHom.IsExpansionOn.{u3, u4, u2, u1, u5} L L' φ M _inst_1 _inst_4] {S : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4}, Eq.{succ u5} (Set.{u5} M) (SetLike.coe.{u5, u5} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) S) M (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u5} L M _inst_1) (FunLike.coe.{succ u5, succ u5, succ u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (fun (_x : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) _x) (RelHomClass.toFunLike.{u5, u5, u5} (OrderEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1)))))) (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) => LE.le.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u1, u5} L' M _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) => LE.le.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u5} (FirstOrder.Language.Substructure.{u3, u4, u5} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u5} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (FirstOrder.Language.LHom.substructureReduct.{u3, u4, u5, u2, u1} L M _inst_1 L' _inst_4 φ _inst_5) S)) (SetLike.coe.{u5, u5} (FirstOrder.Language.Substructure.{u2, u1, u5} L' M _inst_4) M (FirstOrder.Language.Substructure.instSetLike.{u2, u1, u5} L' M _inst_4) S)
+Case conversion may be inaccurate. Consider using '#align first_order.language.Lhom.coe_substructure_reduct FirstOrder.Language.LHom.coe_substructureReductₓ'. -/
 @[simp]
 theorem coe_substructureReduct {S : L'.Substructure M} : (φ.substructureReduct S : Set M) = ↑S :=
   rfl
@@ -741,6 +1205,7 @@ end Lhom
 
 namespace Substructure
 
+#print FirstOrder.Language.Substructure.withConstants /-
 /-- Turns any substructure containing a constant set `A` into a `L[[A]]`-substructure. -/
 def withConstants (S : L.Substructure M) {A : Set M} (h : A ⊆ S) : L[[A]].Substructure M
     where
@@ -752,19 +1217,30 @@ def withConstants (S : L.Substructure M) {A : Set M} (h : A ⊆ S) : L[[A]].Subs
       · exact fun _ _ => h f.2
       · exact isEmptyElim f
 #align first_order.language.substructure.with_constants FirstOrder.Language.Substructure.withConstants
+-/
 
 variable {A : Set M} {s : Set M} (h : A ⊆ S)
 
+#print FirstOrder.Language.Substructure.mem_withConstants /-
 @[simp]
 theorem mem_withConstants {x : M} : x ∈ S.withConstants h ↔ x ∈ S :=
   Iff.rfl
 #align first_order.language.substructure.mem_with_constants FirstOrder.Language.Substructure.mem_withConstants
+-/
 
+#print FirstOrder.Language.Substructure.coe_withConstants /-
 @[simp]
 theorem coe_withConstants : (S.withConstants h : Set M) = ↑S :=
   rfl
 #align first_order.language.substructure.coe_with_constants FirstOrder.Language.Substructure.coe_withConstants
+-/
 
+/- warning: first_order.language.substructure.reduct_with_constants -> FirstOrder.Language.Substructure.reduct_withConstants is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {A : Set.{u3} M} (h : HasSubset.Subset.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) A ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)), Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))))) (fun (_x : RelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (RelEmbedding.hasCoeToFun.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, max u1 u3, u2} L M _inst_1 (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)) (FirstOrder.Language.lhomWithConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) (FirstOrder.Language.withConstants_expansion.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) S
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {A : Set.{u3} M} (h : HasSubset.Subset.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) A (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S)), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (fun (_x : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) => LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) => LE.le.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) => LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (FirstOrder.Language.LHom.substructureReduct.{u1, u2, u3, max u1 u3, u2} L M _inst_1 (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A)) (FirstOrder.Language.lhomWithConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) (FirstOrder.Language.withConstants_expansion.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 S A h)) S
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.reduct_with_constants FirstOrder.Language.Substructure.reduct_withConstantsₓ'. -/
 @[simp]
 theorem reduct_withConstants : (L.lhomWithConstants A).substructureReduct (S.withConstants h) = S :=
   by
@@ -772,6 +1248,7 @@ theorem reduct_withConstants : (L.lhomWithConstants A).substructureReduct (S.wit
   simp
 #align first_order.language.substructure.reduct_with_constants FirstOrder.Language.Substructure.reduct_withConstants
 
+#print FirstOrder.Language.Substructure.subset_closure_withConstants /-
 theorem subset_closure_withConstants : A ⊆ closure (L[[A]]) s :=
   by
   intro a ha
@@ -779,7 +1256,14 @@ theorem subset_closure_withConstants : A ⊆ closure (L[[A]]) s :=
   let a' : L[[A]].Constants := Sum.inr ⟨a, ha⟩
   exact constants_mem a'
 #align first_order.language.substructure.subset_closure_with_constants FirstOrder.Language.Substructure.subset_closure_withConstants
+-/
 
+/- warning: first_order.language.substructure.closure_with_constants_eq -> FirstOrder.Language.Substructure.closure_withConstants_eq is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {A : Set.{u3} M} {s : Set.{u3} M}, Eq.{succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A)))))))) (FirstOrder.Language.Substructure.closure.{max u1 u3, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (coeSort.{succ u3, succ (succ u3)} (Set.{u3} M) Type.{u3} (Set.hasCoeToSort.{u3} M) A) (FirstOrder.Language.paramsStructure.{u3} M A))) s) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.hasUnion.{u3} M) A s)) A (HasSubset.Subset.trans.{u3} (Set.{u3} M) (Set.hasSubset.{u3} M) (Set.hasSubset.Subset.isTrans.{u3} M) A (Union.union.{u3} (Set.{u3} M) (Set.hasUnion.{u3} M) A s) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.hasUnion.{u3} M) A s))) (Set.subset_union_left.{u3} M A s) (FirstOrder.Language.Substructure.subset_closure.{u1, u2, u3} L M _inst_1 (Union.union.{u3} (Set.{u3} M) (Set.hasUnion.{u3} M) A s))))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {A : Set.{u3} M} {s : Set.{u3} M}, Eq.{succ u3} (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) (FirstOrder.Language.Substructure.instCompleteLattice.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A)))))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) M (FirstOrder.Language.Substructure.instSetLike.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A)))) (FirstOrder.Language.Substructure.closure.{max u3 u1, u2, u3} (FirstOrder.Language.withConstants.{u1, u2, u3} L (Set.Elem.{u3} M A)) M (FirstOrder.Language.withConstantsStructure.{u1, u2, u3, u3} L M _inst_1 (Set.Elem.{u3} M A) (FirstOrder.Language.paramsStructure.{u3} M A))) s) (FirstOrder.Language.Substructure.withConstants.{u1, u2, u3} L M _inst_1 (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.instUnionSet.{u3} M) A s)) A (HasSubset.Subset.trans.{u3} (Set.{u3} M) (Set.instHasSubsetSet.{u3} M) (Set.instIsTransSetSubsetInstHasSubsetSet.{u3} M) A (Union.union.{u3} (Set.{u3} M) (Set.instUnionSet.{u3} M) A s) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) (LowerAdjoint.toFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.instCompleteBooleanAlgebraSet.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1)))) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) (Union.union.{u3} (Set.{u3} M) (Set.instUnionSet.{u3} M) A s))) (Set.subset_union_left.{u3} M A s) (FirstOrder.Language.Substructure.subset_closure.{u1, u2, u3} L M _inst_1 (Union.union.{u3} (Set.{u3} M) (Set.instUnionSet.{u3} M) A s))))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.closure_with_constants_eq FirstOrder.Language.Substructure.closure_withConstants_eqₓ'. -/
 theorem closure_withConstants_eq :
     closure (L[[A]]) s =
       (closure L (A ∪ s)).withConstants ((A.subset_union_left s).trans subset_closure) :=
@@ -799,12 +1283,15 @@ namespace Hom
 
 open Substructure
 
+#print FirstOrder.Language.Hom.domRestrict /-
 /-- The restriction of a first-order hom to a substructure `s ⊆ M` gives a hom `s → N`. -/
 @[simps]
 def domRestrict (f : M →[L] N) (p : L.Substructure M) : p →[L] N :=
   f.comp p.Subtype.toHom
 #align first_order.language.hom.dom_restrict FirstOrder.Language.Hom.domRestrict
+-/
 
+#print FirstOrder.Language.Hom.codRestrict /-
 /-- A first-order hom `f : M → N` whose values lie in a substructure `p ⊆ N` can be restricted to a
 hom `M → p`. -/
 @[simps]
@@ -813,69 +1300,141 @@ def codRestrict (p : L.Substructure N) (f : M →[L] N) (h : ∀ c, f c ∈ p) :
   toFun c := ⟨f c, h c⟩
   map_rel' n R x h := f.map_rel R x h
 #align first_order.language.hom.cod_restrict FirstOrder.Language.Hom.codRestrict
+-/
 
+/- warning: first_order.language.hom.comp_cod_restrict -> FirstOrder.Language.Hom.comp_codRestrict is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (p : FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (h : forall (b : N), Membership.Mem.{u5, u5} P (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (SetLike.hasMem.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) (coeFn.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3) => N -> P) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u4, u5} L N P _inst_2 _inst_3) g b) p), Eq.{max (succ u3) (succ u5)} (FirstOrder.Language.Hom.{u1, u2, u3, u5} L M (coeSort.{succ u5, succ (succ u5)} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u5} L P _inst_3 p)) (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 (coeSort.{succ u5, succ (succ u5)} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) p) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u5} L P _inst_3 p) (FirstOrder.Language.Hom.codRestrict.{u1, u2, u4, u5} L N P _inst_2 _inst_3 p g h) f) (FirstOrder.Language.Hom.codRestrict.{u1, u2, u3, u5} L M P _inst_1 _inst_3 p (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f) (fun (b : M) => h (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f b)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} {P : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u1} L P] (f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u3, u4, u2, u1} L N P _inst_2 _inst_3) (p : FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (h : forall (b : N), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : N) => P) b) (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (FirstOrder.Language.Hom.{u3, u4, u2, u1} L N P _inst_2 _inst_3) N (fun (_x : N) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : N) => P) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u2, u1} L N P _inst_2 _inst_3) g b) p), Eq.{max (succ u5) (succ u1)} (FirstOrder.Language.Hom.{u3, u4, u5, u1} L M (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u3, u4, u1} L P _inst_3 p)) (FirstOrder.Language.Hom.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) x p)) (FirstOrder.Language.Substructure.inducedStructure.{u3, u4, u1} L P _inst_3 p) (FirstOrder.Language.Hom.codRestrict.{u3, u4, u2, u1} L N P _inst_2 _inst_3 p g h) f) (FirstOrder.Language.Hom.codRestrict.{u3, u4, u5, u1} L M P _inst_1 _inst_3 p (FirstOrder.Language.Hom.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 P _inst_3 g f) (fun (b : M) => h (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2) f b)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.comp_cod_restrict FirstOrder.Language.Hom.comp_codRestrictₓ'. -/
 @[simp]
 theorem comp_codRestrict (f : M →[L] N) (g : N →[L] P) (p : L.Substructure P) (h : ∀ b, g b ∈ p) :
     ((codRestrict p g h).comp f : M →[L] p) = codRestrict p (g.comp f) fun b => h _ :=
   ext fun b => rfl
 #align first_order.language.hom.comp_cod_restrict FirstOrder.Language.Hom.comp_codRestrict
 
+/- warning: first_order.language.hom.subtype_comp_cod_restrict -> FirstOrder.Language.Hom.subtype_comp_codRestrict is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (h : forall (b : M), Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f b) p), Eq.{max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p) N _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u4, u4} L (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) N (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p) _inst_2 (FirstOrder.Language.Substructure.subtype.{u1, u2, u4} L N _inst_2 p)) (FirstOrder.Language.Hom.codRestrict.{u1, u2, u3, u4} L M N _inst_1 _inst_2 p f h)) f
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (h : forall (b : M), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) b) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f b) p), Eq.{max (succ u4) (succ u1)} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (FirstOrder.Language.Hom.comp.{u2, u3, u4, u1, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p) N _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u1, u1} L (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) N (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p) _inst_2 (FirstOrder.Language.Substructure.subtype.{u2, u3, u1} L N _inst_2 p)) (FirstOrder.Language.Hom.codRestrict.{u2, u3, u4, u1} L M N _inst_1 _inst_2 p f h)) f
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.subtype_comp_cod_restrict FirstOrder.Language.Hom.subtype_comp_codRestrictₓ'. -/
 @[simp]
 theorem subtype_comp_codRestrict (f : M →[L] N) (p : L.Substructure N) (h : ∀ b, f b ∈ p) :
     p.Subtype.toHom.comp (codRestrict p f h) = f :=
   ext fun b => rfl
 #align first_order.language.hom.subtype_comp_cod_restrict FirstOrder.Language.Hom.subtype_comp_codRestrict
 
+#print FirstOrder.Language.Hom.range /-
 /-- The range of a first-order hom `f : M → N` is a submodule of `N`.
 See Note [range copy pattern]. -/
 def range (f : M →[L] N) : L.Substructure N :=
   (map f ⊤).copy (Set.range f) Set.image_univ.symm
 #align first_order.language.hom.range FirstOrder.Language.Hom.range
+-/
 
+/- warning: first_order.language.hom.range_coe -> FirstOrder.Language.Hom.range_coe is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (Set.{u4} N) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (HasLiftT.mk.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (CoeTCₓ.coe.{succ u4, succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Set.{u4} N) (SetLike.Set.hasCoeT.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)) (Set.range.{u4, succ u3} N M (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (Set.{u1} N) (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)) (Set.range.{u1, succ u4} N M (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f))
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_coe FirstOrder.Language.Hom.range_coeₓ'. -/
 theorem range_coe (f : M →[L] N) : (range f : Set N) = Set.range f :=
   rfl
 #align first_order.language.hom.range_coe FirstOrder.Language.Hom.range_coe
 
+/- warning: first_order.language.hom.mem_range -> FirstOrder.Language.Hom.mem_range is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {x : N}, Iff (Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)) (Exists.{succ u3} M (fun (y : M) => Eq.{succ u4} N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f y) x))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {x : N}, Iff (Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)) (Exists.{succ u4} M (fun (y : M) => Eq.{succ u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) y) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f y) x))
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.mem_range FirstOrder.Language.Hom.mem_rangeₓ'. -/
 @[simp]
 theorem mem_range {f : M →[L] N} {x} : x ∈ range f ↔ ∃ y, f y = x :=
   Iff.rfl
 #align first_order.language.hom.mem_range FirstOrder.Language.Hom.mem_range
 
+/- warning: first_order.language.hom.range_eq_map -> FirstOrder.Language.Hom.range_eq_map is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_eq_map FirstOrder.Language.Hom.range_eq_mapₓ'. -/
 theorem range_eq_map (f : M →[L] N) : f.range = map f ⊤ :=
   by
   ext
   simp
 #align first_order.language.hom.range_eq_map FirstOrder.Language.Hom.range_eq_map
 
+/- warning: first_order.language.hom.mem_range_self -> FirstOrder.Language.Hom.mem_range_self is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (x : M), Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (x : M), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) x) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f x) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.mem_range_self FirstOrder.Language.Hom.mem_range_selfₓ'. -/
 theorem mem_range_self (f : M →[L] N) (x : M) : f x ∈ f.range :=
   ⟨x, rfl⟩
 #align first_order.language.hom.mem_range_self FirstOrder.Language.Hom.mem_range_self
 
+#print FirstOrder.Language.Hom.range_id /-
 @[simp]
 theorem range_id : range (id L M) = ⊤ :=
   SetLike.coe_injective Set.range_id
 #align first_order.language.hom.range_id FirstOrder.Language.Hom.range_id
+-/
 
+/- warning: first_order.language.hom.range_comp -> FirstOrder.Language.Hom.range_comp is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3), Eq.{succ u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (FirstOrder.Language.Hom.range.{u1, u2, u3, u5} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f)) (FirstOrder.Language.Substructure.map.{u1, u2, u4, u5} L N P _inst_2 _inst_3 g (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} {P : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u1} L P] (f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u3, u4, u2, u1} L N P _inst_2 _inst_3), Eq.{succ u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (FirstOrder.Language.Hom.range.{u3, u4, u5, u1} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 P _inst_3 g f)) (FirstOrder.Language.Substructure.map.{u3, u4, u2, u1} L N P _inst_2 _inst_3 g (FirstOrder.Language.Hom.range.{u3, u4, u5, u2} L M N _inst_1 _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_comp FirstOrder.Language.Hom.range_compₓ'. -/
 theorem range_comp (f : M →[L] N) (g : N →[L] P) : range (g.comp f : M →[L] P) = map g (range f) :=
   SetLike.coe_injective (Set.range_comp g f)
 #align first_order.language.hom.range_comp FirstOrder.Language.Hom.range_comp
 
+/- warning: first_order.language.hom.range_comp_le_range -> FirstOrder.Language.Hom.range_comp_le_range is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u1, u2, u4, u5} L N P _inst_2 _inst_3), LE.le.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (Preorder.toLE.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (PartialOrder.toPreorder.{u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (SetLike.partialOrder.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)))) (FirstOrder.Language.Hom.range.{u1, u2, u3, u5} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f)) (FirstOrder.Language.Hom.range.{u1, u2, u4, u5} L N P _inst_2 _inst_3 g)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} {P : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u1} L P] (f : FirstOrder.Language.Hom.{u3, u4, u5, u2} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Hom.{u3, u4, u2, u1} L N P _inst_2 _inst_3), LE.le.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (FirstOrder.Language.Substructure.instCompleteLattice.{u3, u4, u1} L P _inst_3))))) (FirstOrder.Language.Hom.range.{u3, u4, u5, u1} L M P _inst_1 _inst_3 (FirstOrder.Language.Hom.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 P _inst_3 g f)) (FirstOrder.Language.Hom.range.{u3, u4, u2, u1} L N P _inst_2 _inst_3 g)
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_comp_le_range FirstOrder.Language.Hom.range_comp_le_rangeₓ'. -/
 theorem range_comp_le_range (f : M →[L] N) (g : N →[L] P) : range (g.comp f : M →[L] P) ≤ range g :=
   SetLike.coe_mono (Set.range_comp_subset_range f g)
 #align first_order.language.hom.range_comp_le_range FirstOrder.Language.Hom.range_comp_le_range
 
+/- warning: first_order.language.hom.range_eq_top -> FirstOrder.Language.Hom.range_eq_top is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, Iff (Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) (Top.top.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u1, u2, u4} L N _inst_2))) (Function.Surjective.{succ u3, succ u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, Iff (Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) (Top.top.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u2, u3, u1} L N _inst_2))) (Function.Surjective.{succ u4, succ u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f))
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_eq_top FirstOrder.Language.Hom.range_eq_topₓ'. -/
 theorem range_eq_top {f : M →[L] N} : range f = ⊤ ↔ Function.Surjective f := by
   rw [SetLike.ext'_iff, range_coe, coe_top, Set.range_iff_surjective]
 #align first_order.language.hom.range_eq_top FirstOrder.Language.Hom.range_eq_top
 
+/- warning: first_order.language.hom.range_le_iff_comap -> FirstOrder.Language.Hom.range_le_iff_comap is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2}, Iff (LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p) (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2}, Iff (LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p) (Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.comap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f p) (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.range_le_iff_comap FirstOrder.Language.Hom.range_le_iff_comapₓ'. -/
 theorem range_le_iff_comap {f : M →[L] N} {p : L.Substructure N} : range f ≤ p ↔ comap f p = ⊤ := by
   rw [range_eq_map, map_le_iff_le_comap, eq_top_iff]
 #align first_order.language.hom.range_le_iff_comap FirstOrder.Language.Hom.range_le_iff_comap
 
+/- warning: first_order.language.hom.map_le_range -> FirstOrder.Language.Hom.map_le_range is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, LE.le.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (Preorder.toLE.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.partialOrder.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)))) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {p : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1}, LE.le.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (Preorder.toLE.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (PartialOrder.toPreorder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteSemilatticeInf.toPartialOrder.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (CompleteLattice.toCompleteSemilatticeInf.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u1} L N _inst_2))))) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f p) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.map_le_range FirstOrder.Language.Hom.map_le_rangeₓ'. -/
 theorem map_le_range {f : M →[L] N} {p : L.Substructure M} : map f p ≤ range f :=
   SetLike.coe_mono (Set.image_subset_range f p)
 #align first_order.language.hom.map_le_range FirstOrder.Language.Hom.map_le_range
 
+#print FirstOrder.Language.Hom.eqLocus /-
 /-- The substructure of elements `x : M` such that `f x = g x` -/
 def eqLocus (f g : M →[L] N) : Substructure L M
     where
@@ -888,19 +1447,38 @@ def eqLocus (f g : M →[L] N) : Substructure L M
       apply hx
     simp [h]
 #align first_order.language.hom.eq_locus FirstOrder.Language.Hom.eqLocus
+-/
 
+/- warning: first_order.language.hom.eq_on_closure -> FirstOrder.Language.Hom.eqOn_closure is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {s : Set.{u3} M}, (Set.EqOn.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) g) s) -> (Set.EqOn.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) g) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {s : Set.{u4} M}, (Set.EqOn.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) g) s) -> (Set.EqOn.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) g) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) s)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.eq_on_closure FirstOrder.Language.Hom.eqOn_closureₓ'. -/
 /-- If two `L.hom`s are equal on a set, then they are equal on its substructure closure. -/
 theorem eqOn_closure {f g : M →[L] N} {s : Set M} (h : Set.EqOn f g s) :
     Set.EqOn f g (closure L s) :=
   show closure L s ≤ f.eqLocus g from closure_le.2 h
 #align first_order.language.hom.eq_on_closure FirstOrder.Language.Hom.eqOn_closure
 
+/- warning: first_order.language.hom.eq_of_eq_on_top -> FirstOrder.Language.Hom.eq_of_eqOn_top is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Set.EqOn.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) g) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1)))) -> (Eq.{max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f g)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Set.EqOn.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) g) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1)))) -> (Eq.{max (succ u4) (succ u1)} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f g)
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.eq_of_eq_on_top FirstOrder.Language.Hom.eq_of_eqOn_topₓ'. -/
 theorem eq_of_eqOn_top {f g : M →[L] N} (h : Set.EqOn f g (⊤ : Substructure L M)) : f = g :=
   ext fun x => h trivial
 #align first_order.language.hom.eq_of_eq_on_top FirstOrder.Language.Hom.eq_of_eqOn_top
 
 variable {s : Set M}
 
+/- warning: first_order.language.hom.eq_of_eq_on_dense -> FirstOrder.Language.Hom.eq_of_eqOn_dense is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] {s : Set.{u3} M}, (Eq.{succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (coeFn.{succ u3, succ u3} (LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (fun (_x : LowerAdjoint.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) => (Set.{u3} M) -> (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1)) (LowerAdjoint.hasCoeToFun.{u3, u3} (Set.{u3} M) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (Set.{u3} M) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} M) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} M) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} M) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} M) (Set.completeBooleanAlgebra.{u3} M))))))) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))))) (FirstOrder.Language.Substructure.closure.{u1, u2, u3} L M _inst_1) s) (Top.top.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u1, u2, u3} L M _inst_1))) -> (forall {f : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2}, (Set.EqOn.{u3, u4} M N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Hom.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) g) s) -> (Eq.{max (succ u3) (succ u4)} (FirstOrder.Language.Hom.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f g))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] {s : Set.{u4} M}, (Eq.{succ u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (LowerAdjoint.toFun.{u4, u4} (Set.{u4} M) (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (PartialOrder.toPreorder.{u4} (Set.{u4} M) (CompleteSemilatticeInf.toPartialOrder.{u4} (Set.{u4} M) (CompleteLattice.toCompleteSemilatticeInf.{u4} (Set.{u4} M) (Order.Coframe.toCompleteLattice.{u4} (Set.{u4} M) (CompleteDistribLattice.toCoframe.{u4} (Set.{u4} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u4} (Set.{u4} M) (Set.instCompleteBooleanAlgebraSet.{u4} M))))))) (PartialOrder.toPreorder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u2, u3, u4} L M _inst_1)))) (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) (FirstOrder.Language.Substructure.closure.{u2, u3, u4} L M _inst_1) s) (Top.top.{u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (FirstOrder.Language.Substructure.instTop.{u2, u3, u4} L M _inst_1))) -> (forall {f : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2} {g : FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2}, (Set.EqOn.{u4, u1} M N (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.5742 : M) => N) _x) (FirstOrder.Language.Hom.funLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2) g) s) -> (Eq.{max (succ u4) (succ u1)} (FirstOrder.Language.Hom.{u2, u3, u4, u1} L M N _inst_1 _inst_2) f g))
+Case conversion may be inaccurate. Consider using '#align first_order.language.hom.eq_of_eq_on_dense FirstOrder.Language.Hom.eq_of_eqOn_denseₓ'. -/
 theorem eq_of_eqOn_dense (hs : closure L s = ⊤) {f g : M →[L] N} (h : s.EqOn f g) : f = g :=
   eq_of_eqOn_top <| hs ▸ eqOn_closure h
 #align first_order.language.hom.eq_of_eq_on_dense FirstOrder.Language.Hom.eq_of_eqOn_dense
@@ -911,17 +1489,26 @@ namespace Embedding
 
 open Substructure
 
+#print FirstOrder.Language.Embedding.domRestrict /-
 /-- The restriction of a first-order embedding to a substructure `s ⊆ M` gives an embedding `s → N`.
 -/
 def domRestrict (f : M ↪[L] N) (p : L.Substructure M) : p ↪[L] N :=
   f.comp p.Subtype
 #align first_order.language.embedding.dom_restrict FirstOrder.Language.Embedding.domRestrict
+-/
 
+/- warning: first_order.language.embedding.dom_restrict_apply -> FirstOrder.Language.Embedding.domRestrict_apply is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x : coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p), Eq.{succ u4} N (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) N (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) N (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) _inst_2) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) N (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) _inst_2) (FirstOrder.Language.Embedding.domRestrict.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (coeSubtype.{succ u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x p))))) x))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (x : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)), Eq.{succ u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) => N) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) N (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) _inst_2) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (fun (_x : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) N (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) _inst_2) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) N (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) _inst_2)) (FirstOrder.Language.Embedding.domRestrict.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f p) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f (Subtype.val.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Set.{u4} M) (Set.instMembershipSet.{u4} M) x (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) p)) x))
+Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.dom_restrict_apply FirstOrder.Language.Embedding.domRestrict_applyₓ'. -/
 @[simp]
 theorem domRestrict_apply (f : M ↪[L] N) (p : L.Substructure M) (x : p) : f.domRestrict p x = f x :=
   rfl
 #align first_order.language.embedding.dom_restrict_apply FirstOrder.Language.Embedding.domRestrict_apply
 
+#print FirstOrder.Language.Embedding.codRestrict /-
 /-- A first-order embedding `f : M → N` whose values lie in a substructure `p ⊆ N` can be restricted
 to an embedding `M → p`. -/
 def codRestrict (p : L.Substructure N) (f : M ↪[L] N) (h : ∀ c, f c ∈ p) : M ↪[L] p
@@ -936,25 +1523,45 @@ def codRestrict (p : L.Substructure N) (f : M ↪[L] N) (h : ∀ c, f c ∈ p) :
     rw [hom.subtype_comp_cod_restrict, ← f.map_rel]
     rfl
 #align first_order.language.embedding.cod_restrict FirstOrder.Language.Embedding.codRestrict
+-/
 
+/- warning: first_order.language.embedding.cod_restrict_apply -> FirstOrder.Language.Embedding.codRestrict_apply is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (p : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) {h : forall (c : M), Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f c) p} (x : M), Eq.{succ u4} N ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) N (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) N (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) N (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) N (coeSubtype.{succ u4} N (fun (x : N) => Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) x p))))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p)) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p)) => M -> (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p)) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p)) (FirstOrder.Language.Embedding.codRestrict.{u1, u2, u3, u4} L M N _inst_1 _inst_2 p f h) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (p : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (f : FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) {h : forall (c : M), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) c) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f c) p} (x : M), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2) p)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p)) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p)) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p))) (FirstOrder.Language.Embedding.codRestrict.{u2, u3, u4, u1} L M N _inst_1 _inst_2 p f h) x)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f x)
+Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.cod_restrict_apply FirstOrder.Language.Embedding.codRestrict_applyₓ'. -/
 @[simp]
 theorem codRestrict_apply (p : L.Substructure N) (f : M ↪[L] N) {h} (x : M) :
     (codRestrict p f h x : N) = f x :=
   rfl
 #align first_order.language.embedding.cod_restrict_apply FirstOrder.Language.Embedding.codRestrict_apply
 
+/- warning: first_order.language.embedding.comp_cod_restrict -> FirstOrder.Language.Embedding.comp_codRestrict is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] [_inst_3 : FirstOrder.Language.Structure.{u1, u2, u5} L P] (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Embedding.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (p : FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (h : forall (b : N), Membership.Mem.{u5, u5} P (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) (SetLike.hasMem.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) (coeFn.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (FirstOrder.Language.Embedding.{u1, u2, u4, u5} L N P _inst_2 _inst_3) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u4, u5} L N P _inst_2 _inst_3) => N -> P) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u4, u5} L N P _inst_2 _inst_3) g b) p), Eq.{max (succ u3) (succ u5)} (FirstOrder.Language.Embedding.{u1, u2, u3, u5} L M (coeSort.{succ u5, succ (succ u5)} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u5} L P _inst_3 p)) (FirstOrder.Language.Embedding.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 (coeSort.{succ u5, succ (succ u5)} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (FirstOrder.Language.Substructure.{u1, u2, u5} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u5} L P _inst_3)) p) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u5} L P _inst_3 p) (FirstOrder.Language.Embedding.codRestrict.{u1, u2, u4, u5} L N P _inst_2 _inst_3 p g h) f) (FirstOrder.Language.Embedding.codRestrict.{u1, u2, u3, u5} L M P _inst_1 _inst_3 p (FirstOrder.Language.Embedding.comp.{u1, u2, u3, u4, u5} L M N _inst_1 _inst_2 P _inst_3 g f) (fun (b : M) => h (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f b)))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u3, u4}} {M : Type.{u5}} {N : Type.{u2}} {P : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u3, u4, u5} L M] [_inst_2 : FirstOrder.Language.Structure.{u3, u4, u2} L N] [_inst_3 : FirstOrder.Language.Structure.{u3, u4, u1} L P] (f : FirstOrder.Language.Embedding.{u3, u4, u5, u2} L M N _inst_1 _inst_2) (g : FirstOrder.Language.Embedding.{u3, u4, u2, u1} L N P _inst_2 _inst_3) (p : FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (h : forall (b : N), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : N) => P) b) (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (FirstOrder.Language.Embedding.{u3, u4, u2, u1} L N P _inst_2 _inst_3) N (fun (_x : N) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : N) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (FirstOrder.Language.Embedding.{u3, u4, u2, u1} L N P _inst_2 _inst_3) N P (FirstOrder.Language.Embedding.embeddingLike.{u3, u4, u2, u1} L N P _inst_2 _inst_3)) g b) p), Eq.{max (succ u5) (succ u1)} (FirstOrder.Language.Embedding.{u3, u4, u5, u1} L M (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u3, u4, u1} L P _inst_3 p)) (FirstOrder.Language.Embedding.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u3, u4, u1} L P _inst_3) P (FirstOrder.Language.Substructure.instSetLike.{u3, u4, u1} L P _inst_3)) x p)) (FirstOrder.Language.Substructure.inducedStructure.{u3, u4, u1} L P _inst_3 p) (FirstOrder.Language.Embedding.codRestrict.{u3, u4, u2, u1} L N P _inst_2 _inst_3 p g h) f) (FirstOrder.Language.Embedding.codRestrict.{u3, u4, u5, u1} L M P _inst_1 _inst_3 p (FirstOrder.Language.Embedding.comp.{u3, u4, u5, u2, u1} L M N _inst_1 _inst_2 P _inst_3 g f) (fun (b : M) => h (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Embedding.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u5) (succ u2), succ u5, succ u2} (FirstOrder.Language.Embedding.{u3, u4, u5, u2} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u3, u4, u5, u2} L M N _inst_1 _inst_2)) f b)))
+Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.comp_cod_restrict FirstOrder.Language.Embedding.comp_codRestrictₓ'. -/
 @[simp]
 theorem comp_codRestrict (f : M ↪[L] N) (g : N ↪[L] P) (p : L.Substructure P) (h : ∀ b, g b ∈ p) :
     ((codRestrict p g h).comp f : M ↪[L] p) = codRestrict p (g.comp f) fun b => h _ :=
   ext fun b => rfl
 #align first_order.language.embedding.comp_cod_restrict FirstOrder.Language.Embedding.comp_codRestrict
 
+/- warning: first_order.language.embedding.subtype_comp_cod_restrict -> FirstOrder.Language.Embedding.subtype_comp_codRestrict is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (h : forall (b : M), Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f b) p), Eq.{max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (FirstOrder.Language.Embedding.comp.{u1, u2, u3, u4, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) p) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 p) N _inst_2 (FirstOrder.Language.Substructure.subtype.{u1, u2, u4} L N _inst_2 p) (FirstOrder.Language.Embedding.codRestrict.{u1, u2, u3, u4} L M N _inst_1 _inst_2 p f h)) f
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (h : forall (b : M), Membership.mem.{u1, u1} ((fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) b) (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f b) p), Eq.{max (succ u4) (succ u1)} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (FirstOrder.Language.Embedding.comp.{u2, u3, u4, u1, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x p)) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 p) N _inst_2 (FirstOrder.Language.Substructure.subtype.{u2, u3, u1} L N _inst_2 p) (FirstOrder.Language.Embedding.codRestrict.{u2, u3, u4, u1} L M N _inst_1 _inst_2 p f h)) f
+Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.subtype_comp_cod_restrict FirstOrder.Language.Embedding.subtype_comp_codRestrictₓ'. -/
 @[simp]
 theorem subtype_comp_codRestrict (f : M ↪[L] N) (p : L.Substructure N) (h : ∀ b, f b ∈ p) :
     p.Subtype.comp (codRestrict p f h) = f :=
   ext fun b => rfl
 #align first_order.language.embedding.subtype_comp_cod_restrict FirstOrder.Language.Embedding.subtype_comp_codRestrict
 
+#print FirstOrder.Language.Embedding.substructureEquivMap /-
 /-- The equivalence between a substructure `s` and its image `s.map f.to_hom`, where `f` is an
   embedding. -/
 noncomputable def substructureEquivMap (f : M ↪[L] N) (s : L.Substructure M) : s ≃[L] s.map f.toHom
@@ -969,13 +1576,21 @@ noncomputable def substructureEquivMap (f : M ↪[L] N) (s : L.Substructure M) :
                 ⟨m, hm⟩).2).2)
   right_inv := fun ⟨n, hn⟩ => Subtype.mk_eq_mk.2 (Classical.choose_spec hn).2
 #align first_order.language.embedding.substructure_equiv_map FirstOrder.Language.Embedding.substructureEquivMap
+-/
 
+/- warning: first_order.language.embedding.substructure_equiv_map_apply -> FirstOrder.Language.Embedding.substructureEquivMap_apply is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (x : coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p), Eq.{succ u4} N ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) N (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) N (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) N (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) N (coeSubtype.{succ u4} N (fun (x : N) => Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)))))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Equiv.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p))) (fun (_x : FirstOrder.Language.Equiv.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p))) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) -> (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Equiv.hasCoeToFun.{u1, u2, u3, u4} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Substructure.map.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Embedding.substructureEquivMap.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f p) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) p) M (coeSubtype.{succ u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.hasMem.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x p))))) x))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (p : FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (x : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (fun (_x : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.8209 : Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (EquivLike.toEmbeddingLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Equiv.instEquivLikeEquiv.{u2, u3, u4, u1} L (Subtype.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) (SetLike.instMembership.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1)) x p)) (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u4} L M _inst_1 p) (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Substructure.map.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) p))))) (FirstOrder.Language.Embedding.substructureEquivMap.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f p) x)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f (Subtype.val.{succ u4} M (fun (x : M) => Membership.mem.{u4, u4} M (Set.{u4} M) (Set.instMembershipSet.{u4} M) x (SetLike.coe.{u4, u4} (FirstOrder.Language.Substructure.{u2, u3, u4} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u4} L M _inst_1) p)) x))
+Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.substructure_equiv_map_apply FirstOrder.Language.Embedding.substructureEquivMap_applyₓ'. -/
 @[simp]
 theorem substructureEquivMap_apply (f : M ↪[L] N) (p : L.Substructure M) (x : p) :
     (f.substructureEquivMap p x : N) = f x :=
   rfl
 #align first_order.language.embedding.substructure_equiv_map_apply FirstOrder.Language.Embedding.substructureEquivMap_apply
 
+#print FirstOrder.Language.Embedding.equivRange /-
 /-- The equivalence between the domain and the range of an embedding `f`. -/
 noncomputable def equivRange (f : M ↪[L] N) : M ≃[L] f.toHom.range
     where
@@ -985,7 +1600,14 @@ noncomputable def equivRange (f : M ↪[L] N) : M ≃[L] f.toHom.range
     f.Injective (Classical.choose_spec (codRestrict f.toHom.range f f.toHom.mem_range_self m).2)
   right_inv := fun ⟨n, hn⟩ => Subtype.mk_eq_mk.2 (Classical.choose_spec hn)
 #align first_order.language.embedding.equiv_range FirstOrder.Language.Embedding.equivRange
+-/
 
+/- warning: first_order.language.embedding.equiv_range_apply -> FirstOrder.Language.Embedding.equivRange_apply is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (x : M), Eq.{succ u4} N ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) N (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) N (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) N (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) N (coeSubtype.{succ u4} N (fun (x : N) => Membership.Mem.{u4, u4} N (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (SetLike.hasMem.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))))))) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Equiv.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)))) (fun (_x : FirstOrder.Language.Equiv.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)))) => M -> (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)))) (FirstOrder.Language.Equiv.hasCoeToFun.{u1, u2, u3, u4} L M (coeSort.{succ u4, succ (succ u4)} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u4} L N _inst_2)) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u4} L N _inst_2 (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)))) (FirstOrder.Language.Embedding.equivRange.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f) x)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u4} L M N _inst_1 _inst_2) => M -> N) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u4} L M N _inst_1 _inst_2) f x)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) (x : M), Eq.{succ u1} N (Subtype.val.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (Set.{u1} N) (Set.instMembershipSet.{u1} N) x (SetLike.coe.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.8209 : M) => Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) (EquivLike.toEmbeddingLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Equiv.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) (FirstOrder.Language.Equiv.instEquivLikeEquiv.{u2, u3, u4, u1} L M (Subtype.{succ u1} N (fun (x : N) => Membership.mem.{u1, u1} N (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (SetLike.instMembership.{u1, u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) N (FirstOrder.Language.Substructure.instSetLike.{u2, u3, u1} L N _inst_2)) x (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))) _inst_1 (FirstOrder.Language.Substructure.inducedStructure.{u2, u3, u1} L N _inst_2 (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Embedding.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)))))) (FirstOrder.Language.Embedding.equivRange.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f) x)) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M (fun (_x : M) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : M) => N) _x) (EmbeddingLike.toFunLike.{max (succ u4) (succ u1), succ u4, succ u1} (FirstOrder.Language.Embedding.{u2, u3, u4, u1} L M N _inst_1 _inst_2) M N (FirstOrder.Language.Embedding.embeddingLike.{u2, u3, u4, u1} L M N _inst_1 _inst_2)) f x)
+Case conversion may be inaccurate. Consider using '#align first_order.language.embedding.equiv_range_apply FirstOrder.Language.Embedding.equivRange_applyₓ'. -/
 @[simp]
 theorem equivRange_apply (f : M ↪[L] N) (x : M) : (f.equivRange x : N) = f x :=
   rfl
@@ -995,6 +1617,12 @@ end Embedding
 
 namespace Equiv
 
+/- warning: first_order.language.equiv.to_hom_range -> FirstOrder.Language.Equiv.toHom_range is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} {N : Type.{u4}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] [_inst_2 : FirstOrder.Language.Structure.{u1, u2, u4} L N] (f : FirstOrder.Language.Equiv.{u1, u2, u3, u4} L M N _inst_1 _inst_2), Eq.{succ u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Hom.range.{u1, u2, u3, u4} L M N _inst_1 _inst_2 (FirstOrder.Language.Equiv.toHom.{u1, u2, u3, u4} L M N _inst_1 _inst_2 f)) (Top.top.{u4} (FirstOrder.Language.Substructure.{u1, u2, u4} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u1, u2, u4} L N _inst_2))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u2, u3}} {M : Type.{u4}} {N : Type.{u1}} [_inst_1 : FirstOrder.Language.Structure.{u2, u3, u4} L M] [_inst_2 : FirstOrder.Language.Structure.{u2, u3, u1} L N] (f : FirstOrder.Language.Equiv.{u2, u3, u4, u1} L M N _inst_1 _inst_2), Eq.{succ u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Hom.range.{u2, u3, u4, u1} L M N _inst_1 _inst_2 (FirstOrder.Language.Equiv.toHom.{u2, u3, u4, u1} L M N _inst_1 _inst_2 f)) (Top.top.{u1} (FirstOrder.Language.Substructure.{u2, u3, u1} L N _inst_2) (FirstOrder.Language.Substructure.instTop.{u2, u3, u1} L N _inst_2))
+Case conversion may be inaccurate. Consider using '#align first_order.language.equiv.to_hom_range FirstOrder.Language.Equiv.toHom_rangeₓ'. -/
 theorem toHom_range (f : M ≃[L] N) : f.toHom.range = ⊤ :=
   by
   ext n
@@ -1006,17 +1634,30 @@ end Equiv
 
 namespace Substructure
 
+/- warning: first_order.language.substructure.inclusion -> FirstOrder.Language.Substructure.inclusion is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T) -> (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T))
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1}, (LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S T) -> (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T))
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.inclusion FirstOrder.Language.Substructure.inclusionₓ'. -/
 /-- The embedding associated to an inclusion of substructures. -/
 def inclusion {S T : L.Substructure M} (h : S ≤ T) : S ↪[L] T :=
   S.Subtype.codRestrict _ fun x => h x.2
 #align first_order.language.substructure.inclusion FirstOrder.Language.Substructure.inclusion
 
+/- warning: first_order.language.substructure.coe_inclusion -> FirstOrder.Language.Substructure.coe_inclusion is a dubious translation:
+lean 3 declaration is
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} (h : LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.partialOrder.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S T), Eq.{succ u3} ((fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) -> (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T)) (FirstOrder.Language.Substructure.inclusion.{u1, u2, u3} L M _inst_1 S T h)) (coeFn.{succ u3, succ u3} (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (fun (_x : FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) => (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) -> (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T)) (FirstOrder.Language.Embedding.hasCoeToFun.{u1, u2, u3, u3} L (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) S) (coeSort.{succ u3, succ (succ u3)} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) T) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (FirstOrder.Language.Substructure.inclusion.{u1, u2, u3} L M _inst_1 S T h)) (Set.inclusion.{u3} M (fun (x : M) => Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) x ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) S)) (fun (x : M) => Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) x ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)))) T)) h)
+but is expected to have type
+  forall {L : FirstOrder.Language.{u1, u2}} {M : Type.{u3}} [_inst_1 : FirstOrder.Language.Structure.{u1, u2, u3} L M] {S : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} {T : FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1} (h : LE.le.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (Preorder.toLE.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (PartialOrder.toPreorder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (FirstOrder.Language.Substructure.instCompleteLattice.{u1, u2, u3} L M _inst_1))))) S T), Eq.{succ u3} (forall (a : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)), (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) a) (FunLike.coe.{succ u3, succ u3, succ u3} (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (fun (_x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) => (fun (a._@.Mathlib.ModelTheory.Basic._hyg.6670 : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) _x) (EmbeddingLike.toFunLike.{succ u3, succ u3, succ u3} (FirstOrder.Language.Embedding.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Embedding.embeddingLike.{u1, u2, u3, u3} L (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x S)) (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) (SetLike.instMembership.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1)) x T)) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 S) (FirstOrder.Language.Substructure.inducedStructure.{u1, u2, u3} L M _inst_1 T))) (FirstOrder.Language.Substructure.inclusion.{u1, u2, u3} L M _inst_1 S T h)) (Set.inclusion.{u3} M (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) S) (SetLike.coe.{u3, u3} (FirstOrder.Language.Substructure.{u1, u2, u3} L M _inst_1) M (FirstOrder.Language.Substructure.instSetLike.{u1, u2, u3} L M _inst_1) T) h)
+Case conversion may be inaccurate. Consider using '#align first_order.language.substructure.coe_inclusion FirstOrder.Language.Substructure.coe_inclusionₓ'. -/
 @[simp]
 theorem coe_inclusion {S T : L.Substructure M} (h : S ≤ T) :
     (inclusion h : S → T) = Set.inclusion h :=
   rfl
 #align first_order.language.substructure.coe_inclusion FirstOrder.Language.Substructure.coe_inclusion
 
+#print FirstOrder.Language.Substructure.range_subtype /-
 theorem range_subtype (S : L.Substructure M) : S.Subtype.toHom.range = S :=
   by
   ext x
@@ -1025,6 +1666,7 @@ theorem range_subtype (S : L.Substructure M) : S.Subtype.toHom.range = S :=
   rintro ⟨⟨y, hy⟩, rfl⟩
   exact hy
 #align first_order.language.substructure.range_subtype FirstOrder.Language.Substructure.range_subtype
+-/
 
 end Substructure

0602c598

bump to nightly-2023-04-13-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

b0c3fa7f

Diff

@@ -724,18 +724,18 @@ def substructureReduct : L'.Substructure M ↪o L.Substructure M
     simp only [SetLike.coe_set_eq] at h
     exact h
   map_rel_iff' S T := Iff.rfl
-#align first_order.language.Lhom.substructure_reduct FirstOrder.Language.Lhom.substructureReduct
+#align first_order.language.Lhom.substructure_reduct FirstOrder.Language.LHom.substructureReduct
 
 @[simp]
 theorem mem_substructureReduct {x : M} {S : L'.Substructure M} :
     x ∈ φ.substructureReduct S ↔ x ∈ S :=
   Iff.rfl
-#align first_order.language.Lhom.mem_substructure_reduct FirstOrder.Language.Lhom.mem_substructureReduct
+#align first_order.language.Lhom.mem_substructure_reduct FirstOrder.Language.LHom.mem_substructureReduct
 
 @[simp]
 theorem coe_substructureReduct {S : L'.Substructure M} : (φ.substructureReduct S : Set M) = ↑S :=
   rfl
-#align first_order.language.Lhom.coe_substructure_reduct FirstOrder.Language.Lhom.coe_substructureReduct
+#align first_order.language.Lhom.coe_substructure_reduct FirstOrder.Language.LHom.coe_substructureReduct
 
 end Lhom

0602c598

bump to nightly-2023-02-28-04

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

2097f8af

Diff

@@ -178,7 +178,7 @@ theorem coe_top : ((⊤ : L.Substructure M) : Set M) = Set.univ :=
 #align first_order.language.substructure.coe_top FirstOrder.Language.Substructure.coe_top
 
 /-- The inf of two substructures is their intersection. -/
-instance : HasInf (L.Substructure M) :=
+instance : Inf (L.Substructure M) :=
   ⟨fun S₁ S₂ =>
     { carrier := S₁ ∩ S₂
       fun_mem := fun n f => (S₁.fun_mem f).inf (S₂.fun_mem f) }⟩

0602c598

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

0602c598

feat(ModelTheory): lift of equivalences between direct limits, and direct limit of system of substructures (#11174)

Define the equivalence between direct limits of isomorphic systems, and the equivalence between the direct limit of a system of substructures and the union of these substructures. Co-authored-by: Aaron Anderson <awainverse@gmail.com>

Co-authored-by: Gabin <68381468+QuinnLesquimau@users.noreply.github.com> Co-authored-by: Johan Commelin <johan@commelin.net>

0d98b682

Diff

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2021 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Aaron Anderson
+Authors: Aaron Anderson, Gabin Kolly
 -/
 import Mathlib.Order.Closure
 import Mathlib.ModelTheory.Semantics
@@ -943,6 +943,11 @@ theorem codRestrict_apply (p : L.Substructure N) (f : M ↪[L] N) {h} (x : M) :
   rfl
 #align first_order.language.embedding.cod_restrict_apply FirstOrder.Language.Embedding.codRestrict_apply
 
+@[simp]
+theorem codRestrict_apply' (p : L.Substructure N) (f : M ↪[L] N) {h} (x : M) :
+    codRestrict p f h x = ⟨f x, h x⟩ :=
+  rfl
+
 @[simp]
 theorem comp_codRestrict (f : M ↪[L] N) (g : N ↪[L] P) (p : L.Substructure P) (h : ∀ b, g b ∈ p) :
     ((codRestrict p g h).comp f : M ↪[L] p) = codRestrict p (g.comp f) fun _ => h _ :=
@@ -978,6 +983,11 @@ theorem substructureEquivMap_apply (f : M ↪[L] N) (p : L.Substructure M) (x :
   rfl
 #align first_order.language.embedding.substructure_equiv_map_apply FirstOrder.Language.Embedding.substructureEquivMap_apply
 
+@[simp]
+theorem subtype_substructureEquivMap (f : M ↪[L] N) (s : L.Substructure M) :
+    (subtype _).comp (f.substructureEquivMap s).toEmbedding = f.comp (subtype _) := by
+  ext; rfl
+
 /-- The equivalence between the domain and the range of an embedding `f`. -/
 noncomputable def equivRange (f : M ↪[L] N) : M ≃[L] f.toHom.range where
   toFun := codRestrict f.toHom.range f f.toHom.mem_range_self
@@ -994,6 +1004,10 @@ theorem equivRange_apply (f : M ↪[L] N) (x : M) : (f.equivRange x : N) = f x :
   rfl
 #align first_order.language.embedding.equiv_range_apply FirstOrder.Language.Embedding.equivRange_apply
 
+@[simp]
+theorem subtype_equivRange (f : M ↪[L] N) : (subtype _).comp f.equivRange.toEmbedding = f := by
+  ext; rfl
+
 end Embedding
 
 namespace Equiv
@@ -1013,6 +1027,9 @@ def inclusion {S T : L.Substructure M} (h : S ≤ T) : S ↪[L] T :=
   S.subtype.codRestrict _ fun x => h x.2
 #align first_order.language.substructure.inclusion FirstOrder.Language.Substructure.inclusion
 
+@[simp]
+theorem inclusion_self (S : L.Substructure M) : inclusion (le_refl S) = Embedding.refl L S := rfl
+
 @[simp]
 theorem coe_inclusion {S T : L.Substructure M} (h : S ≤ T) :
     (inclusion h : S → T) = Set.inclusion h :=

0602c598

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -44,7 +44,6 @@ namespace FirstOrder
 namespace Language
 
 variable {L : Language.{u, v}} {M : Type w} {N P : Type*}
-
 variable [L.Structure M] [L.Structure N] [L.Structure P]
 
 open FirstOrder Cardinal

0602c598

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

@@ -221,7 +221,7 @@ theorem mem_sInf {S : Set (L.Substructure M)} {x : M} : x ∈ sInf S ↔ ∀ p 
 #align first_order.language.substructure.mem_Inf FirstOrder.Language.Substructure.mem_sInf
 
 theorem mem_iInf {ι : Sort*} {S : ι → L.Substructure M} {x : M} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i :=
-  by simp only [iInf, mem_sInf, Set.forall_range_iff]
+  by simp only [iInf, mem_sInf, Set.forall_mem_range]
 #align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_iInf
 
 @[simp, norm_cast]

0602c598

chore: uneven spacing for ⟨ ⟩ (#10014)

This cleans up instances of

⟨ foo, bar⟩

and

⟨foo, bar ⟩

where spaces a on the inside one side, but not on the other side. Fixing this by removing the extra space.

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

909ee227

Diff

@@ -107,7 +107,7 @@ namespace Substructure
 attribute [coe] Substructure.carrier
 
 instance instSetLike : SetLike (L.Substructure M) M :=
-  ⟨Substructure.carrier, fun p q h => by cases p; cases q; congr ⟩
+  ⟨Substructure.carrier, fun p q h => by cases p; cases q; congr⟩
 #align first_order.language.substructure.set_like FirstOrder.Language.Substructure.instSetLike
 
 /-- See Note [custom simps projection] -/

0602c598

chore(ModelTheory/ElementarySubstructures): Split elementary substructures into their own file (#9026)

This PR splits the file ModelTheory/ElementaryMaps into two files, moving elementary substructure code into ModelTheory/ElementarySubstructures, to make room for new API on those.

Two basic lemmas, FirstOrder.Language.Substructure.realize_boundedFormula_top and FirstOrder.Language.Substructure.realize_formula_top, are instead moved to the file ModelTheory/Substructures.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com> Co-authored-by: Aaron Anderson <65780815+awainverse@users.noreply.github.com>

a5732e8f

Diff

@@ -685,6 +685,21 @@ theorem coe_topEquiv :
   rfl
 #align first_order.language.substructure.coe_top_equiv FirstOrder.Language.Substructure.coe_topEquiv
 
+@[simp]
+theorem realize_boundedFormula_top {α : Type*} {n : ℕ} {φ : L.BoundedFormula α n}
+    {v : α → (⊤ : L.Substructure M)} {xs : Fin n → (⊤ : L.Substructure M)} :
+    φ.Realize v xs ↔ φ.Realize (((↑) : _ → M) ∘ v) ((↑) ∘ xs) := by
+  rw [← Substructure.topEquiv.realize_boundedFormula φ]
+  simp
+#align first_order.language.substructure.realize_bounded_formula_top FirstOrder.Language.Substructure.realize_boundedFormula_top
+
+@[simp]
+theorem realize_formula_top {α : Type*} {φ : L.Formula α} {v : α → (⊤ : L.Substructure M)} :
+    φ.Realize v ↔ φ.Realize (((↑) : (⊤ : L.Substructure M) → M) ∘ v) := by
+  rw [← Substructure.topEquiv.realize_formula φ]
+  simp
+#align first_order.language.substructure.realize_formula_top FirstOrder.Language.Substructure.realize_formula_top
+
 /-- A dependent version of `Substructure.closure_induction`. -/
 @[elab_as_elim]
 theorem closure_induction' (s : Set M) {p : ∀ x, x ∈ closure L s → Prop}

0602c598

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -43,7 +43,7 @@ namespace FirstOrder
 
 namespace Language
 
-variable {L : Language.{u, v}} {M : Type w} {N P : Type _}
+variable {L : Language.{u, v}} {M : Type w} {N P : Type*}
 
 variable [L.Structure M] [L.Structure N] [L.Structure P]
 
@@ -138,7 +138,7 @@ end Substructure
 
 variable {S : L.Substructure M}
 
-theorem Term.realize_mem {α : Type _} (t : L.Term α) (xs : α → M) (h : ∀ a, xs a ∈ S) :
+theorem Term.realize_mem {α : Type*} (t : L.Term α) (xs : α → M) (h : ∀ a, xs a ∈ S) :
     t.realize xs ∈ S := by
   induction' t with a n f ts ih
   · exact h a
@@ -220,12 +220,12 @@ theorem mem_sInf {S : Set (L.Substructure M)} {x : M} : x ∈ sInf S ↔ ∀ p 
   Set.mem_iInter₂
 #align first_order.language.substructure.mem_Inf FirstOrder.Language.Substructure.mem_sInf
 
-theorem mem_iInf {ι : Sort _} {S : ι → L.Substructure M} {x : M} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i :=
+theorem mem_iInf {ι : Sort*} {S : ι → L.Substructure M} {x : M} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i :=
   by simp only [iInf, mem_sInf, Set.forall_range_iff]
 #align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_iInf
 
 @[simp, norm_cast]
-theorem coe_iInf {ι : Sort _} {S : ι → L.Substructure M} :
+theorem coe_iInf {ι : Sort*} {S : ι → L.Substructure M} :
     ((⨅ i, S i : L.Substructure M) : Set M) = ⋂ i, (S i : Set M) := by
   simp only [iInf, coe_sInf, Set.biInter_range]
 #align first_order.language.substructure.coe_infi FirstOrder.Language.Substructure.coe_iInf
@@ -511,7 +511,7 @@ theorem map_sup (S T : L.Substructure M) (f : M →[L] N) : (S ⊔ T).map f = S.
   (gc_map_comap f).l_sup
 #align first_order.language.substructure.map_sup FirstOrder.Language.Substructure.map_sup
 
-theorem map_iSup {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure M) :
+theorem map_iSup {ι : Sort*} (f : M →[L] N) (s : ι → L.Substructure M) :
     (iSup s).map f = ⨆ i, (s i).map f :=
   (gc_map_comap f).l_iSup
 #align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_iSup
@@ -521,7 +521,7 @@ theorem comap_inf (S T : L.Substructure N) (f : M →[L] N) :
   (gc_map_comap f).u_inf
 #align first_order.language.substructure.comap_inf FirstOrder.Language.Substructure.comap_inf
 
-theorem comap_iInf {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure N) :
+theorem comap_iInf {ι : Sort*} (f : M →[L] N) (s : ι → L.Substructure N) :
     (iInf s).comap f = ⨅ i, (s i).comap f :=
   (gc_map_comap f).u_iInf
 #align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_iInf
@@ -554,7 +554,7 @@ theorem closure_image (f : M →[L] N) : closure L (f '' s) = map f (closure L s
 
 section GaloisCoinsertion
 
-variable {ι : Type _} {f : M →[L] N} (hf : Function.Injective f)
+variable {ι : Type*} {f : M →[L] N} (hf : Function.Injective f)
 
 /-- `map f` and `comap f` form a `GaloisCoinsertion` when `f` is injective. -/
 def gciMapComap : GaloisCoinsertion (map f) (comap f) :=
@@ -603,7 +603,7 @@ end GaloisCoinsertion
 
 section GaloisInsertion
 
-variable {ι : Type _} {f : M →[L] N} (hf : Function.Surjective f)
+variable {ι : Type*} {f : M →[L] N} (hf : Function.Surjective f)
 
 /-- `map f` and `comap f` form a `GaloisInsertion` when `f` is surjective. -/
 def giMapComap : GaloisInsertion (map f) (comap f) :=

0602c598

chore: fix grammar mistakes (#6121)

a16538af

Diff

@@ -24,7 +24,7 @@ substructure `s` under the homomorphism `f`, as a substructure.
 * `FirstOrder.Language.Substructure.map` is defined so that `s.map f` is the image of the
 substructure `s` under the homomorphism `f`, as a substructure.
 * `FirstOrder.Language.Hom.range` is defined so that `f.range` is the range of the
-the homomorphism `f`, as a substructure.
+homomorphism `f`, as a substructure.
 * `FirstOrder.Language.Hom.domRestrict` and `FirstOrder.Language.Hom.codRestrict` restrict
 the domain and codomain respectively of first-order homomorphisms to substructures.
 * `FirstOrder.Language.Embedding.domRestrict` and `FirstOrder.Language.Embedding.codRestrict`

0602c598

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module model_theory.substructures
-! leanprover-community/mathlib commit 0602c59878ff3d5f71dea69c2d32ccf2e93e5398
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Order.Closure
 import Mathlib.ModelTheory.Semantics
 import Mathlib.ModelTheory.Encoding
 
+#align_import model_theory.substructures from "leanprover-community/mathlib"@"0602c59878ff3d5f71dea69c2d32ccf2e93e5398"
+
 /-!
 # First-Order Substructures
 This file defines substructures of first-order structures in a similar manner to the various

0602c598

fix: precedence of # (#5623)

d450fcd7

Diff

@@ -320,15 +320,15 @@ theorem mem_closure_iff_exists_term {x : M} :
   rw [← SetLike.mem_coe, coe_closure_eq_range_term_realize, mem_range]
 #align first_order.language.substructure.mem_closure_iff_exists_term FirstOrder.Language.Substructure.mem_closure_iff_exists_term
 
-theorem lift_card_closure_le_card_term : Cardinal.lift.{max u w} (#closure L s) ≤ (#L.Term s) := by
+theorem lift_card_closure_le_card_term : Cardinal.lift.{max u w} #(closure L s) ≤ #(L.Term s) := by
   rw [← SetLike.coe_sort_coe, coe_closure_eq_range_term_realize]
-  rw [← Cardinal.lift_id'.{w, max u w} (#L.Term s)]
+  rw [← Cardinal.lift_id'.{w, max u w} #(L.Term s)]
   exact Cardinal.mk_range_le_lift
 #align first_order.language.substructure.lift_card_closure_le_card_term FirstOrder.Language.Substructure.lift_card_closure_le_card_term
 
 theorem lift_card_closure_le :
-    Cardinal.lift.{u, w} (#closure L s) ≤
-      max ℵ₀ (Cardinal.lift.{u, w} (#s) + Cardinal.lift.{w, u} (#Σi, L.Functions i)) := by
+    Cardinal.lift.{u, w} #(closure L s) ≤
+      max ℵ₀ (Cardinal.lift.{u, w} #s + Cardinal.lift.{w, u} #(Σi, L.Functions i)) := by
   rw [← lift_umax]
   refine' lift_card_closure_le_card_term.trans (Term.card_le.trans _)
   rw [mk_sum, lift_umax.{w, u}]

0602c598

doc: fix the docs on ModelTheory/* (#3968)

a2ab29ce

Diff

@@ -26,7 +26,7 @@ the least substructure of `M` containing `s`.
 substructure `s` under the homomorphism `f`, as a substructure.
 * `FirstOrder.Language.Substructure.map` is defined so that `s.map f` is the image of the
 substructure `s` under the homomorphism `f`, as a substructure.
-* `FirstOrder.Language.Hom.range` is defined so that `f.map` is the range of the
+* `FirstOrder.Language.Hom.range` is defined so that `f.range` is the range of the
 the homomorphism `f`, as a substructure.
 * `FirstOrder.Language.Hom.domRestrict` and `FirstOrder.Language.Hom.codRestrict` restrict
 the domain and codomain respectively of first-order homomorphisms to substructures.
@@ -663,7 +663,7 @@ instance inducedStructure {S : L.Substructure M} : L.Structure S where
 set_option linter.uppercaseLean3 false in
 #align first_order.language.substructure.induced_Structure FirstOrder.Language.Substructure.inducedStructure
 
-/-- The natural embedding of an `L.substructure` of `M` into `M`. -/
+/-- The natural embedding of an `L.Substructure` of `M` into `M`. -/
 def subtype (S : L.Substructure M) : S ↪[L] M where
   toFun := (↑)
   inj' := Subtype.coe_injective

0602c598

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

@@ -85,9 +85,9 @@ theorem inf (hs : ClosedUnder f s) (ht : ClosedUnder f t) : ClosedUnder f (s ⊓
 
 variable {S : Set (Set M)}
 
-theorem infₛ (hS : ∀ s, s ∈ S → ClosedUnder f s) : ClosedUnder f (infₛ S) := fun x h s hs =>
+theorem sInf (hS : ∀ s, s ∈ S → ClosedUnder f s) : ClosedUnder f (sInf S) := fun x h s hs =>
   hS s hs x fun i => h i s hs
-#align first_order.language.closed_under.Inf FirstOrder.Language.ClosedUnder.infₛ
+#align first_order.language.closed_under.Inf FirstOrder.Language.ClosedUnder.sInf
 
 end ClosedUnder
 
@@ -205,7 +205,7 @@ instance instInfSet : InfSet (L.Substructure M) :=
   ⟨fun s =>
     { carrier := ⋂ t ∈ s, (t : Set M)
       fun_mem := fun {n} f =>
-        ClosedUnder.infₛ
+        ClosedUnder.sInf
           (by
             rintro _ ⟨t, rfl⟩
             by_cases h : t ∈ s
@@ -214,37 +214,37 @@ instance instInfSet : InfSet (L.Substructure M) :=
 #align first_order.language.substructure.has_Inf FirstOrder.Language.Substructure.instInfSet
 
 @[simp, norm_cast]
-theorem coe_infₛ (S : Set (L.Substructure M)) :
-    ((infₛ S : L.Substructure M) : Set M) = ⋂ s ∈ S, (s : Set M) :=
+theorem coe_sInf (S : Set (L.Substructure M)) :
+    ((sInf S : L.Substructure M) : Set M) = ⋂ s ∈ S, (s : Set M) :=
   rfl
-#align first_order.language.substructure.coe_Inf FirstOrder.Language.Substructure.coe_infₛ
+#align first_order.language.substructure.coe_Inf FirstOrder.Language.Substructure.coe_sInf
 
-theorem mem_infₛ {S : Set (L.Substructure M)} {x : M} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p :=
-  Set.mem_interᵢ₂
-#align first_order.language.substructure.mem_Inf FirstOrder.Language.Substructure.mem_infₛ
+theorem mem_sInf {S : Set (L.Substructure M)} {x : M} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p :=
+  Set.mem_iInter₂
+#align first_order.language.substructure.mem_Inf FirstOrder.Language.Substructure.mem_sInf
 
-theorem mem_infᵢ {ι : Sort _} {S : ι → L.Substructure M} {x : M} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i :=
-  by simp only [infᵢ, mem_infₛ, Set.forall_range_iff]
-#align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_infᵢ
+theorem mem_iInf {ι : Sort _} {S : ι → L.Substructure M} {x : M} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i :=
+  by simp only [iInf, mem_sInf, Set.forall_range_iff]
+#align first_order.language.substructure.mem_infi FirstOrder.Language.Substructure.mem_iInf
 
 @[simp, norm_cast]
-theorem coe_infᵢ {ι : Sort _} {S : ι → L.Substructure M} :
+theorem coe_iInf {ι : Sort _} {S : ι → L.Substructure M} :
     ((⨅ i, S i : L.Substructure M) : Set M) = ⋂ i, (S i : Set M) := by
-  simp only [infᵢ, coe_infₛ, Set.binterᵢ_range]
-#align first_order.language.substructure.coe_infi FirstOrder.Language.Substructure.coe_infᵢ
+  simp only [iInf, coe_sInf, Set.biInter_range]
+#align first_order.language.substructure.coe_infi FirstOrder.Language.Substructure.coe_iInf
 
 /-- Substructures of a structure form a complete lattice. -/
 instance instCompleteLattice : CompleteLattice (L.Substructure M) :=
   { completeLatticeOfInf (L.Substructure M) fun _ =>
       IsGLB.of_image
         (fun {S T : L.Substructure M} => show (S : Set M) ≤ T ↔ S ≤ T from SetLike.coe_subset_coe)
-        isGLB_binfᵢ with
+        isGLB_biInf with
     le := (· ≤ ·)
     lt := (· < ·)
     top := ⊤
     le_top := fun _ x _ => mem_top x
     inf := (· ⊓ ·)
-    infₛ := InfSet.infₛ
+    sInf := InfSet.sInf
     le_inf := fun _a _b _c ha hb _x hx => ⟨ha hx, hb hx⟩
     inf_le_left := fun _ _ _ => And.left
     inf_le_right := fun _ _ _ => And.right }
@@ -254,14 +254,14 @@ variable (L)
 
 /-- The `L.Substructure` generated by a set. -/
 def closure : LowerAdjoint ((↑) : L.Substructure M → Set M) :=
-  ⟨fun s => infₛ { S | s ⊆ S }, fun _ _ =>
-    ⟨Set.Subset.trans fun _x hx => mem_infₛ.2 fun _S hS => hS hx, fun h => infₛ_le h⟩⟩
+  ⟨fun s => sInf { S | s ⊆ S }, fun _ _ =>
+    ⟨Set.Subset.trans fun _x hx => mem_sInf.2 fun _S hS => hS hx, fun h => sInf_le h⟩⟩
 #align first_order.language.substructure.closure FirstOrder.Language.Substructure.closure
 
 variable {L} {s : Set M}
 
 theorem mem_closure {x : M} : x ∈ closure L s ↔ ∀ S : L.Substructure M, s ⊆ S → x ∈ S :=
-  mem_infₛ
+  mem_sInf
 #align first_order.language.substructure.mem_closure FirstOrder.Language.Substructure.mem_closure
 
 /-- The substructure generated by a set includes the set. -/
@@ -305,7 +305,7 @@ theorem coe_closure_eq_range_term_realize :
     simp only [Term.realize, fun i => Classical.choose_spec (hx i)]⟩
   change _ = (S : Set M)
   rw [← SetLike.ext'_iff]
-  refine' closure_eq_of_le (fun x hx => ⟨var ⟨x, hx⟩, rfl⟩) (le_infₛ fun S' hS' => _)
+  refine' closure_eq_of_le (fun x hx => ⟨var ⟨x, hx⟩, rfl⟩) (le_sInf fun S' hS' => _)
   · rintro _ ⟨t, rfl⟩
     exact t.realize_mem _ fun i => hS' i.2
 #align first_order.language.substructure.coe_closure_eq_range_term_realize FirstOrder.Language.Substructure.coe_closure_eq_range_term_realize
@@ -396,7 +396,7 @@ theorem closure_union (s t : Set M) : closure L (s ∪ t) = closure L s ⊔ clos
 #align first_order.language.substructure.closure_union FirstOrder.Language.Substructure.closure_union
 
 theorem closure_unionᵢ {ι} (s : ι → Set M) : closure L (⋃ i, s i) = ⨆ i, closure L (s i) :=
-  (Substructure.gi L M).gc.l_supᵢ
+  (Substructure.gi L M).gc.l_iSup
 #align first_order.language.substructure.closure_Union FirstOrder.Language.Substructure.closure_unionᵢ
 
 instance small_bot : Small.{u} (⊥ : L.Substructure M) := by
@@ -514,20 +514,20 @@ theorem map_sup (S T : L.Substructure M) (f : M →[L] N) : (S ⊔ T).map f = S.
   (gc_map_comap f).l_sup
 #align first_order.language.substructure.map_sup FirstOrder.Language.Substructure.map_sup
 
-theorem map_supᵢ {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure M) :
-    (supᵢ s).map f = ⨆ i, (s i).map f :=
-  (gc_map_comap f).l_supᵢ
-#align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_supᵢ
+theorem map_iSup {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure M) :
+    (iSup s).map f = ⨆ i, (s i).map f :=
+  (gc_map_comap f).l_iSup
+#align first_order.language.substructure.map_supr FirstOrder.Language.Substructure.map_iSup
 
 theorem comap_inf (S T : L.Substructure N) (f : M →[L] N) :
     (S ⊓ T).comap f = S.comap f ⊓ T.comap f :=
   (gc_map_comap f).u_inf
 #align first_order.language.substructure.comap_inf FirstOrder.Language.Substructure.comap_inf
 
-theorem comap_infᵢ {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure N) :
-    (infᵢ s).comap f = ⨅ i, (s i).comap f :=
-  (gc_map_comap f).u_infᵢ
-#align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_infᵢ
+theorem comap_iInf {ι : Sort _} (f : M →[L] N) (s : ι → L.Substructure N) :
+    (iInf s).comap f = ⨅ i, (s i).comap f :=
+  (gc_map_comap f).u_iInf
+#align first_order.language.substructure.comap_infi FirstOrder.Language.Substructure.comap_iInf
 
 @[simp]
 theorem map_bot (f : M →[L] N) : (⊥ : L.Substructure M).map f = ⊥ :=
@@ -580,19 +580,19 @@ theorem comap_inf_map_of_injective (S T : L.Substructure M) : (S.map f ⊓ T.map
   (gciMapComap hf).u_inf_l _ _
 #align first_order.language.substructure.comap_inf_map_of_injective FirstOrder.Language.Substructure.comap_inf_map_of_injective
 
-theorem comap_infᵢ_map_of_injective (S : ι → L.Substructure M) :
-    (⨅ i, (S i).map f).comap f = infᵢ S :=
-  (gciMapComap hf).u_infᵢ_l _
-#align first_order.language.substructure.comap_infi_map_of_injective FirstOrder.Language.Substructure.comap_infᵢ_map_of_injective
+theorem comap_iInf_map_of_injective (S : ι → L.Substructure M) :
+    (⨅ i, (S i).map f).comap f = iInf S :=
+  (gciMapComap hf).u_iInf_l _
+#align first_order.language.substructure.comap_infi_map_of_injective FirstOrder.Language.Substructure.comap_iInf_map_of_injective
 
 theorem comap_sup_map_of_injective (S T : L.Substructure M) : (S.map f ⊔ T.map f).comap f = S ⊔ T :=
   (gciMapComap hf).u_sup_l _ _
 #align first_order.language.substructure.comap_sup_map_of_injective FirstOrder.Language.Substructure.comap_sup_map_of_injective
 
-theorem comap_supᵢ_map_of_injective (S : ι → L.Substructure M) :
-    (⨆ i, (S i).map f).comap f = supᵢ S :=
-  (gciMapComap hf).u_supᵢ_l _
-#align first_order.language.substructure.comap_supr_map_of_injective FirstOrder.Language.Substructure.comap_supᵢ_map_of_injective
+theorem comap_iSup_map_of_injective (S : ι → L.Substructure M) :
+    (⨆ i, (S i).map f).comap f = iSup S :=
+  (gciMapComap hf).u_iSup_l _
+#align first_order.language.substructure.comap_supr_map_of_injective FirstOrder.Language.Substructure.comap_iSup_map_of_injective
 
 theorem map_le_map_iff_of_injective {S T : L.Substructure M} : S.map f ≤ T.map f ↔ S ≤ T :=
   (gciMapComap hf).l_le_l_iff
@@ -632,20 +632,20 @@ theorem map_inf_comap_of_surjective (S T : L.Substructure N) :
   (giMapComap hf).l_inf_u _ _
 #align first_order.language.substructure.map_inf_comap_of_surjective FirstOrder.Language.Substructure.map_inf_comap_of_surjective
 
-theorem map_infᵢ_comap_of_surjective (S : ι → L.Substructure N) :
-    (⨅ i, (S i).comap f).map f = infᵢ S :=
-  (giMapComap hf).l_infᵢ_u _
-#align first_order.language.substructure.map_infi_comap_of_surjective FirstOrder.Language.Substructure.map_infᵢ_comap_of_surjective
+theorem map_iInf_comap_of_surjective (S : ι → L.Substructure N) :
+    (⨅ i, (S i).comap f).map f = iInf S :=
+  (giMapComap hf).l_iInf_u _
+#align first_order.language.substructure.map_infi_comap_of_surjective FirstOrder.Language.Substructure.map_iInf_comap_of_surjective
 
 theorem map_sup_comap_of_surjective (S T : L.Substructure N) :
     (S.comap f ⊔ T.comap f).map f = S ⊔ T :=
   (giMapComap hf).l_sup_u _ _
 #align first_order.language.substructure.map_sup_comap_of_surjective FirstOrder.Language.Substructure.map_sup_comap_of_surjective
 
-theorem map_supᵢ_comap_of_surjective (S : ι → L.Substructure N) :
-    (⨆ i, (S i).comap f).map f = supᵢ S :=
-  (giMapComap hf).l_supᵢ_u _
-#align first_order.language.substructure.map_supr_comap_of_surjective FirstOrder.Language.Substructure.map_supᵢ_comap_of_surjective
+theorem map_iSup_comap_of_surjective (S : ι → L.Substructure N) :
+    (⨆ i, (S i).comap f).map f = iSup S :=
+  (giMapComap hf).l_iSup_u _
+#align first_order.language.substructure.map_supr_comap_of_surjective FirstOrder.Language.Substructure.map_iSup_comap_of_surjective
 
 theorem comap_le_comap_iff_of_surjective {S T : L.Substructure N} : S.comap f ≤ T.comap f ↔ S ≤ T :=
   (giMapComap hf).u_le_u_iff

0602c598

feat: port ModelTheory.Substructures (#3913)

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

6e1a2ec5

`model_theory.substructures` ⟷ `Mathlib.ModelTheory.Substructures`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 362

model_theory.substructures ⟷ Mathlib.ModelTheory.Substructures

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 362

`model_theory.substructures` ⟷ `Mathlib.ModelTheory.Substructures`