linear_algebra.projection ⟷ Mathlib.LinearAlgebra.Projection

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

@@ -70,7 +70,7 @@ theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl
   · rw [codisjoint_iff_le_sup]
     intro x hx
     rw [mem_sup']
-    refine' ⟨f x, ⟨x - f x, _⟩, add_sub_cancel'_right _ _⟩
+    refine' ⟨f x, ⟨x - f x, _⟩, add_sub_cancel _ _⟩
     rw [mem_ker, LinearMap.map_sub, hf, sub_self]
 #align linear_map.is_compl_of_proj LinearMap.isCompl_of_proj
 -/

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

@@ -65,7 +65,7 @@ theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl
   constructor
   · rw [disjoint_iff_inf_le]
     rintro x ⟨hpx, hfx⟩
-    erw [SetLike.mem_coe, mem_ker, hf ⟨x, hpx⟩, mk_eq_zero] at hfx 
+    erw [SetLike.mem_coe, mem_ker, hf ⟨x, hpx⟩, mk_eq_zero] at hfx
     simp only [hfx, SetLike.mem_coe, zero_mem]
   · rw [codisjoint_iff_le_sup]
     intro x hx

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

@@ -484,7 +484,7 @@ of `E` to `p` and fixes every element of `p`.
 The definition allow more generally any `fun_like` type and not just linear maps, so that it can be
 used for example with `continuous_linear_map` or `matrix`.
 -/
-structure IsProj {F : Type _} [FunLike F M fun _ => M] (f : F) : Prop where
+structure IsProj {F : Type _} [DFunLike F M fun _ => M] (f : F) : Prop where
   map_mem : ∀ x, f x ∈ m
   map_id : ∀ x ∈ m, f x = x
 #align linear_map.is_proj LinearMap.IsProj

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.LinearAlgebra.Quotient
-import Mathbin.LinearAlgebra.Prod
+import LinearAlgebra.Quotient
+import LinearAlgebra.Prod
 
 #align_import linear_algebra.projection from "leanprover-community/mathlib"@"3dadefa3f544b1db6214777fe47910739b54c66a"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module linear_algebra.projection
-! leanprover-community/mathlib commit 3dadefa3f544b1db6214777fe47910739b54c66a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Quotient
 import Mathbin.LinearAlgebra.Prod
 
+#align_import linear_algebra.projection from "leanprover-community/mathlib"@"3dadefa3f544b1db6214777fe47910739b54c66a"
+
 /-!
 # Projection to a subspace
 

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

@@ -47,17 +47,22 @@ variable {p}
 
 open Submodule
 
+#print LinearMap.ker_id_sub_eq_of_proj /-
 theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
     ker (id - p.Subtype.comp f) = p := by
   ext x
   simp only [comp_apply, mem_ker, subtype_apply, sub_apply, id_apply, sub_eq_zero]
   exact ⟨fun h => h.symm ▸ Submodule.coe_mem _, fun hx => by erw [hf ⟨x, hx⟩, Subtype.coe_mk]⟩
 #align linear_map.ker_id_sub_eq_of_proj LinearMap.ker_id_sub_eq_of_proj
+-/
 
+#print LinearMap.range_eq_of_proj /-
 theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f = ⊤ :=
   range_eq_top.2 fun x => ⟨x, hf x⟩
 #align linear_map.range_eq_of_proj LinearMap.range_eq_of_proj
+-/
 
+#print LinearMap.isCompl_of_proj /-
 theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl p f.ker :=
   by
   constructor
@@ -71,6 +76,7 @@ theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl
     refine' ⟨f x, ⟨x - f x, _⟩, add_sub_cancel'_right _ _⟩
     rw [mem_ker, LinearMap.map_sub, hf, sub_self]
 #align linear_map.is_compl_of_proj LinearMap.isCompl_of_proj
+-/
 
 end LinearMap
 
@@ -78,6 +84,7 @@ namespace Submodule
 
 open LinearMap
 
+#print Submodule.quotientEquivOfIsCompl /-
 /-- If `q` is a complement of `p`, then `M/p ≃ q`. -/
 def quotientEquivOfIsCompl (h : IsCompl p q) : (E ⧸ p) ≃ₗ[R] q :=
   LinearEquiv.symm <|
@@ -85,25 +92,33 @@ def quotientEquivOfIsCompl (h : IsCompl p q) : (E ⧸ p) ≃ₗ[R] q :=
       ⟨by rw [← ker_eq_bot, ker_comp, ker_mkq, disjoint_iff_comap_eq_bot.1 h.symm.disjoint], by
         rw [← range_eq_top, range_comp, range_subtype, map_mkq_eq_top, h.sup_eq_top]⟩
 #align submodule.quotient_equiv_of_is_compl Submodule.quotientEquivOfIsCompl
+-/
 
+#print Submodule.quotientEquivOfIsCompl_symm_apply /-
 @[simp]
 theorem quotientEquivOfIsCompl_symm_apply (h : IsCompl p q) (x : q) :
     (quotientEquivOfIsCompl p q h).symm x = Quotient.mk x :=
   rfl
 #align submodule.quotient_equiv_of_is_compl_symm_apply Submodule.quotientEquivOfIsCompl_symm_apply
+-/
 
+#print Submodule.quotientEquivOfIsCompl_apply_mk_coe /-
 @[simp]
 theorem quotientEquivOfIsCompl_apply_mk_coe (h : IsCompl p q) (x : q) :
     quotientEquivOfIsCompl p q h (Quotient.mk x) = x :=
   (quotientEquivOfIsCompl p q h).apply_symm_apply x
 #align submodule.quotient_equiv_of_is_compl_apply_mk_coe Submodule.quotientEquivOfIsCompl_apply_mk_coe
+-/
 
+#print Submodule.mk_quotientEquivOfIsCompl_apply /-
 @[simp]
 theorem mk_quotientEquivOfIsCompl_apply (h : IsCompl p q) (x : E ⧸ p) :
     (Quotient.mk (quotientEquivOfIsCompl p q h x) : E ⧸ p) = x :=
   (quotientEquivOfIsCompl p q h).symm_apply_apply x
 #align submodule.mk_quotient_equiv_of_is_compl_apply Submodule.mk_quotientEquivOfIsCompl_apply
+-/
 
+#print Submodule.prodEquivOfIsCompl /-
 /-- If `q` is a complement of `p`, then `p × q` is isomorphic to `E`. It is the unique
 linear map `f : E → p` such that `f x = x` for `x ∈ p` and `f x = 0` for `x ∈ q`. -/
 def prodEquivOfIsCompl (h : IsCompl p q) : (p × q) ≃ₗ[R] E :=
@@ -115,31 +130,41 @@ def prodEquivOfIsCompl (h : IsCompl p q) : (p × q) ≃ₗ[R] E :=
     exact h.1
   · rw [← range_eq_top, ← sup_eq_range, h.sup_eq_top]
 #align submodule.prod_equiv_of_is_compl Submodule.prodEquivOfIsCompl
+-/
 
+#print Submodule.coe_prodEquivOfIsCompl /-
 @[simp]
 theorem coe_prodEquivOfIsCompl (h : IsCompl p q) :
     (prodEquivOfIsCompl p q h : p × q →ₗ[R] E) = p.Subtype.coprod q.Subtype :=
   rfl
 #align submodule.coe_prod_equiv_of_is_compl Submodule.coe_prodEquivOfIsCompl
+-/
 
+#print Submodule.coe_prodEquivOfIsCompl' /-
 @[simp]
 theorem coe_prodEquivOfIsCompl' (h : IsCompl p q) (x : p × q) :
     prodEquivOfIsCompl p q h x = x.1 + x.2 :=
   rfl
 #align submodule.coe_prod_equiv_of_is_compl' Submodule.coe_prodEquivOfIsCompl'
+-/
 
+#print Submodule.prodEquivOfIsCompl_symm_apply_left /-
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_left (h : IsCompl p q) (x : p) :
     (prodEquivOfIsCompl p q h).symm x = (x, 0) :=
   (prodEquivOfIsCompl p q h).symm_apply_eq.2 <| by simp
 #align submodule.prod_equiv_of_is_compl_symm_apply_left Submodule.prodEquivOfIsCompl_symm_apply_left
+-/
 
+#print Submodule.prodEquivOfIsCompl_symm_apply_right /-
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_right (h : IsCompl p q) (x : q) :
     (prodEquivOfIsCompl p q h).symm x = (0, x) :=
   (prodEquivOfIsCompl p q h).symm_apply_eq.2 <| by simp
 #align submodule.prod_equiv_of_is_compl_symm_apply_right Submodule.prodEquivOfIsCompl_symm_apply_right
+-/
 
+#print Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero /-
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
     ((prodEquivOfIsCompl p q h).symm x).1 = 0 ↔ x ∈ q :=
@@ -148,7 +173,9 @@ theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
   rw [coe_prod_equiv_of_is_compl', Submodule.add_mem_iff_left _ (Submodule.coe_mem _),
     mem_right_iff_eq_zero_of_disjoint h.disjoint]
 #align submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero
+-/
 
+#print Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero /-
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_snd_eq_zero (h : IsCompl p q) {x : E} :
     ((prodEquivOfIsCompl p q h).symm x).2 = 0 ↔ x ∈ p :=
@@ -157,72 +184,98 @@ theorem prodEquivOfIsCompl_symm_apply_snd_eq_zero (h : IsCompl p q) {x : E} :
   rw [coe_prod_equiv_of_is_compl', Submodule.add_mem_iff_right _ (Submodule.coe_mem _),
     mem_left_iff_eq_zero_of_disjoint h.disjoint]
 #align submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero
+-/
 
+#print Submodule.prodComm_trans_prodEquivOfIsCompl /-
 @[simp]
 theorem prodComm_trans_prodEquivOfIsCompl (h : IsCompl p q) :
     LinearEquiv.prodComm R q p ≪≫ₗ prodEquivOfIsCompl p q h = prodEquivOfIsCompl q p h.symm :=
   LinearEquiv.ext fun _ => add_comm _ _
 #align submodule.prod_comm_trans_prod_equiv_of_is_compl Submodule.prodComm_trans_prodEquivOfIsCompl
+-/
 
+#print Submodule.linearProjOfIsCompl /-
 /-- Projection to a submodule along its complement. -/
 def linearProjOfIsCompl (h : IsCompl p q) : E →ₗ[R] p :=
   LinearMap.fst R p q ∘ₗ ↑(prodEquivOfIsCompl p q h).symm
 #align submodule.linear_proj_of_is_compl Submodule.linearProjOfIsCompl
+-/
 
 variable {p q}
 
+#print Submodule.linearProjOfIsCompl_apply_left /-
 @[simp]
 theorem linearProjOfIsCompl_apply_left (h : IsCompl p q) (x : p) :
     linearProjOfIsCompl p q h x = x := by simp [linear_proj_of_is_compl]
 #align submodule.linear_proj_of_is_compl_apply_left Submodule.linearProjOfIsCompl_apply_left
+-/
 
+#print Submodule.linearProjOfIsCompl_range /-
 @[simp]
 theorem linearProjOfIsCompl_range (h : IsCompl p q) : (linearProjOfIsCompl p q h).range = ⊤ :=
   range_eq_of_proj (linearProjOfIsCompl_apply_left h)
 #align submodule.linear_proj_of_is_compl_range Submodule.linearProjOfIsCompl_range
+-/
 
+#print Submodule.linearProjOfIsCompl_apply_eq_zero_iff /-
 @[simp]
 theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
     linearProjOfIsCompl p q h x = 0 ↔ x ∈ q := by simp [linear_proj_of_is_compl]
 #align submodule.linear_proj_of_is_compl_apply_eq_zero_iff Submodule.linearProjOfIsCompl_apply_eq_zero_iff
+-/
 
+#print Submodule.linearProjOfIsCompl_apply_right' /-
 theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q) :
     linearProjOfIsCompl p q h x = 0 :=
   (linearProjOfIsCompl_apply_eq_zero_iff h).2 hx
 #align submodule.linear_proj_of_is_compl_apply_right' Submodule.linearProjOfIsCompl_apply_right'
+-/
 
+#print Submodule.linearProjOfIsCompl_apply_right /-
 @[simp]
 theorem linearProjOfIsCompl_apply_right (h : IsCompl p q) (x : q) :
     linearProjOfIsCompl p q h x = 0 :=
   linearProjOfIsCompl_apply_right' h x x.2
 #align submodule.linear_proj_of_is_compl_apply_right Submodule.linearProjOfIsCompl_apply_right
+-/
 
+#print Submodule.linearProjOfIsCompl_ker /-
 @[simp]
 theorem linearProjOfIsCompl_ker (h : IsCompl p q) : (linearProjOfIsCompl p q h).ker = q :=
   ext fun x => mem_ker.trans (linearProjOfIsCompl_apply_eq_zero_iff h)
 #align submodule.linear_proj_of_is_compl_ker Submodule.linearProjOfIsCompl_ker
+-/
 
+#print Submodule.linearProjOfIsCompl_comp_subtype /-
 theorem linearProjOfIsCompl_comp_subtype (h : IsCompl p q) :
     (linearProjOfIsCompl p q h).comp p.Subtype = id :=
   LinearMap.ext <| linearProjOfIsCompl_apply_left h
 #align submodule.linear_proj_of_is_compl_comp_subtype Submodule.linearProjOfIsCompl_comp_subtype
+-/
 
+#print Submodule.linearProjOfIsCompl_idempotent /-
 theorem linearProjOfIsCompl_idempotent (h : IsCompl p q) (x : E) :
     linearProjOfIsCompl p q h (linearProjOfIsCompl p q h x) = linearProjOfIsCompl p q h x :=
   linearProjOfIsCompl_apply_left h _
 #align submodule.linear_proj_of_is_compl_idempotent Submodule.linearProjOfIsCompl_idempotent
+-/
 
+#print Submodule.existsUnique_add_of_isCompl_prod /-
 theorem existsUnique_add_of_isCompl_prod (hc : IsCompl p q) (x : E) :
     ∃! u : p × q, (u.fst : E) + u.snd = x :=
   (prodEquivOfIsCompl _ _ hc).toEquiv.Bijective.ExistsUnique _
 #align submodule.exists_unique_add_of_is_compl_prod Submodule.existsUnique_add_of_isCompl_prod
+-/
 
+#print Submodule.existsUnique_add_of_isCompl /-
 theorem existsUnique_add_of_isCompl (hc : IsCompl p q) (x : E) :
     ∃ (u : p) (v : q), (u : E) + v = x ∧ ∀ (r : p) (s : q), (r : E) + s = x → r = u ∧ s = v :=
   let ⟨u, hu₁, hu₂⟩ := existsUnique_add_of_isCompl_prod hc x
   ⟨u.1, u.2, hu₁, fun r s hrs => Prod.eq_iff_fst_eq_snd_eq.1 (hu₂ ⟨r, s⟩ hrs)⟩
 #align submodule.exists_unique_add_of_is_compl Submodule.existsUnique_add_of_isCompl
+-/
 
+#print Submodule.linear_proj_add_linearProjOfIsCompl_eq_self /-
 theorem linear_proj_add_linearProjOfIsCompl_eq_self (hpq : IsCompl p q) (x : E) :
     (p.linearProjOfIsCompl q hpq x + q.linearProjOfIsCompl p hpq.symm x : E) = x :=
   by
@@ -230,6 +283,7 @@ theorem linear_proj_add_linearProjOfIsCompl_eq_self (hpq : IsCompl p q) (x : E)
   rw [← prod_comm_trans_prod_equiv_of_is_compl _ _ hpq]
   exact (prod_equiv_of_is_compl _ _ hpq).apply_symm_apply x
 #align submodule.linear_proj_add_linear_proj_of_is_compl_eq_self Submodule.linear_proj_add_linearProjOfIsCompl_eq_self
+-/
 
 end Submodule
 
@@ -237,24 +291,31 @@ namespace LinearMap
 
 open Submodule
 
+#print LinearMap.ofIsCompl /-
 /-- Given linear maps `φ` and `ψ` from complement submodules, `of_is_compl` is
 the induced linear map over the entire module. -/
 def ofIsCompl {p q : Submodule R E} (h : IsCompl p q) (φ : p →ₗ[R] F) (ψ : q →ₗ[R] F) : E →ₗ[R] F :=
   LinearMap.coprod φ ψ ∘ₗ ↑(Submodule.prodEquivOfIsCompl _ _ h).symm
 #align linear_map.of_is_compl LinearMap.ofIsCompl
+-/
 
 variable {p q}
 
+#print LinearMap.ofIsCompl_left_apply /-
 @[simp]
 theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (u : p) :
     ofIsCompl h φ ψ (u : E) = φ u := by simp [of_is_compl]
 #align linear_map.of_is_compl_left_apply LinearMap.ofIsCompl_left_apply
+-/
 
+#print LinearMap.ofIsCompl_right_apply /-
 @[simp]
 theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (v : q) :
     ofIsCompl h φ ψ (v : E) = ψ v := by simp [of_is_compl]
 #align linear_map.of_is_compl_right_apply LinearMap.ofIsCompl_right_apply
+-/
 
+#print LinearMap.ofIsCompl_eq /-
 theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : ∀ u, φ u = χ u) (hψ : ∀ u, ψ u = χ u) : ofIsCompl h φ ψ = χ :=
   by
@@ -262,34 +323,44 @@ theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F}
   obtain ⟨_, _, rfl, _⟩ := exists_unique_add_of_is_compl h x
   simp [of_is_compl, hφ, hψ]
 #align linear_map.of_is_compl_eq LinearMap.ofIsCompl_eq
+-/
 
+#print LinearMap.ofIsCompl_eq' /-
 theorem ofIsCompl_eq' (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : φ = χ.comp p.Subtype) (hψ : ψ = χ.comp q.Subtype) : ofIsCompl h φ ψ = χ :=
   ofIsCompl_eq h (fun _ => hφ.symm ▸ rfl) fun _ => hψ.symm ▸ rfl
 #align linear_map.of_is_compl_eq' LinearMap.ofIsCompl_eq'
+-/
 
+#print LinearMap.ofIsCompl_zero /-
 @[simp]
 theorem ofIsCompl_zero (h : IsCompl p q) : (ofIsCompl h 0 0 : E →ₗ[R] F) = 0 :=
   ofIsCompl_eq _ (fun _ => rfl) fun _ => rfl
 #align linear_map.of_is_compl_zero LinearMap.ofIsCompl_zero
+-/
 
+#print LinearMap.ofIsCompl_add /-
 @[simp]
 theorem ofIsCompl_add (h : IsCompl p q) {φ₁ φ₂ : p →ₗ[R] F} {ψ₁ ψ₂ : q →ₗ[R] F} :
     ofIsCompl h (φ₁ + φ₂) (ψ₁ + ψ₂) = ofIsCompl h φ₁ ψ₁ + ofIsCompl h φ₂ ψ₂ :=
   ofIsCompl_eq _ (by simp) (by simp)
 #align linear_map.of_is_compl_add LinearMap.ofIsCompl_add
+-/
 
+#print LinearMap.ofIsCompl_smul /-
 @[simp]
 theorem ofIsCompl_smul {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E]
     {F : Type _} [AddCommGroup F] [Module R F] {p q : Submodule R E} (h : IsCompl p q)
     {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (c : R) : ofIsCompl h (c • φ) (c • ψ) = c • ofIsCompl h φ ψ :=
   ofIsCompl_eq _ (by simp) (by simp)
 #align linear_map.of_is_compl_smul LinearMap.ofIsCompl_smul
+-/
 
 section
 
 variable {R₁ : Type _} [CommRing R₁] [Module R₁ E] [Module R₁ F]
 
+#print LinearMap.ofIsComplProd /-
 /-- The linear map from `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` to `E →ₗ[R₁] F`. -/
 def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
     (p →ₗ[R₁] F) × (q →ₗ[R₁] F) →ₗ[R₁] E →ₗ[R₁] F
@@ -298,13 +369,17 @@ def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
   map_add' := by intro φ ψ; rw [Prod.snd_add, Prod.fst_add, of_is_compl_add]
   map_smul' := by intro c φ; simp [Prod.smul_snd, Prod.smul_fst, of_is_compl_smul]
 #align linear_map.of_is_compl_prod LinearMap.ofIsComplProd
+-/
 
+#print LinearMap.ofIsComplProd_apply /-
 @[simp]
 theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
     (φ : (p →ₗ[R₁] F) × (q →ₗ[R₁] F)) : ofIsComplProd h φ = ofIsCompl h φ.1 φ.2 :=
   rfl
 #align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_apply
+-/
 
+#print LinearMap.ofIsComplProdEquiv /-
 /-- The natural linear equivalence between `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` and `E →ₗ[R₁] F`. -/
 def ofIsComplProdEquiv {p q : Submodule R₁ E} (h : IsCompl p q) :
     ((p →ₗ[R₁] F) × (q →ₗ[R₁] F)) ≃ₗ[R₁] E →ₗ[R₁] F :=
@@ -319,9 +394,11 @@ def ofIsComplProdEquiv {p q : Submodule R₁ E} (h : IsCompl p q) :
       obtain ⟨a, b, hab, _⟩ := exists_unique_add_of_is_compl h x
       rw [← hab]; simp }
 #align linear_map.of_is_compl_prod_equiv LinearMap.ofIsComplProdEquiv
+-/
 
 end
 
+#print LinearMap.linearProjOfIsCompl_of_proj /-
 @[simp]
 theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x) :
     p.linearProjOfIsCompl f.ker (isCompl_of_proj hf) = f :=
@@ -331,7 +408,9 @@ theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x
   rcases mem_sup'.1 this with ⟨x, y, rfl⟩
   simp [hf]
 #align linear_map.linear_proj_of_is_compl_of_proj LinearMap.linearProjOfIsCompl_of_proj
+-/
 
+#print LinearMap.equivProdOfSurjectiveOfIsCompl /-
 /-- If `f : E →ₗ[R] F` and `g : E →ₗ[R] G` are two surjective linear maps and
 their kernels are complement of each other, then `x ↦ (f x, g x)` defines
 a linear equivalence `E ≃ₗ[R] F × G`. -/
@@ -341,20 +420,25 @@ def equivProdOfSurjectiveOfIsCompl (f : E →ₗ[R] F) (g : E →ₗ[R] G) (hf :
     ⟨by simp [← ker_eq_bot, hfg.inf_eq_bot], by rw [← range_eq_top];
       simp [range_prod_eq hfg.sup_eq_top, *]⟩
 #align linear_map.equiv_prod_of_surjective_of_is_compl LinearMap.equivProdOfSurjectiveOfIsCompl
+-/
 
+#print LinearMap.coe_equivProdOfSurjectiveOfIsCompl /-
 @[simp]
 theorem coe_equivProdOfSurjectiveOfIsCompl {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
     (hg : g.range = ⊤) (hfg : IsCompl f.ker g.ker) :
     (equivProdOfSurjectiveOfIsCompl f g hf hg hfg : E →ₗ[R] F × G) = f.Prod g :=
   rfl
 #align linear_map.coe_equiv_prod_of_surjective_of_is_compl LinearMap.coe_equivProdOfSurjectiveOfIsCompl
+-/
 
+#print LinearMap.equivProdOfSurjectiveOfIsCompl_apply /-
 @[simp]
 theorem equivProdOfSurjectiveOfIsCompl_apply {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
     (hg : g.range = ⊤) (hfg : IsCompl f.ker g.ker) (x : E) :
     equivProdOfSurjectiveOfIsCompl f g hf hg hfg x = (f x, g x) :=
   rfl
 #align linear_map.equiv_prod_of_surjective_of_is_compl_apply LinearMap.equivProdOfSurjectiveOfIsCompl_apply
+-/
 
 end LinearMap
 
@@ -362,6 +446,7 @@ namespace Submodule
 
 open LinearMap
 
+#print Submodule.isComplEquivProj /-
 /-- Equivalence between submodules `q` such that `is_compl p q` and linear maps `f : E →ₗ[R] p`
 such that `∀ x : p, f x = x`. -/
 def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p, f x = x }
@@ -371,18 +456,23 @@ def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p
   left_inv := fun ⟨q, hq⟩ => by simp only [linear_proj_of_is_compl_ker, Subtype.coe_mk]
   right_inv := fun ⟨f, hf⟩ => Subtype.eq <| f.linearProjOfIsCompl_of_proj hf
 #align submodule.is_compl_equiv_proj Submodule.isComplEquivProj
+-/
 
+#print Submodule.coe_isComplEquivProj_apply /-
 @[simp]
 theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
     (p.isComplEquivProj q : E →ₗ[R] p) = linearProjOfIsCompl p q q.2 :=
   rfl
 #align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_apply
+-/
 
+#print Submodule.coe_isComplEquivProj_symm_apply /-
 @[simp]
 theorem coe_isComplEquivProj_symm_apply (f : { f : E →ₗ[R] p // ∀ x : p, f x = x }) :
     (p.isComplEquivProj.symm f : Submodule R E) = (f : E →ₗ[R] p).ker :=
   rfl
 #align submodule.coe_is_compl_equiv_proj_symm_apply Submodule.coe_isComplEquivProj_symm_apply
+-/
 
 end Submodule
 
@@ -403,6 +493,7 @@ structure IsProj {F : Type _} [FunLike F M fun _ => M] (f : F) : Prop where
 #align linear_map.is_proj LinearMap.IsProj
 -/
 
+#print LinearMap.isProj_iff_idempotent /-
 theorem isProj_iff_idempotent (f : M →ₗ[S] M) : (∃ p : Submodule S M, IsProj p f) ↔ f ∘ₗ f = f :=
   by
   constructor
@@ -411,36 +502,48 @@ theorem isProj_iff_idempotent (f : M →ₗ[S] M) : (∃ p : Submodule S M, IsPr
     · intro x; exact mem_range_self f x
     · intro x hx; obtain ⟨y, hy⟩ := mem_range.1 hx; rw [← hy, ← comp_apply, h]
 #align linear_map.is_proj_iff_idempotent LinearMap.isProj_iff_idempotent
+-/
 
 namespace IsProj
 
 variable {p m}
 
+#print LinearMap.IsProj.codRestrict /-
 /-- Restriction of the codomain of a projection of onto a subspace `p` to `p` instead of the whole
 space.
 -/
 def codRestrict {f : M →ₗ[S] M} (h : IsProj m f) : M →ₗ[S] m :=
   f.codRestrict m h.map_mem
 #align linear_map.is_proj.cod_restrict LinearMap.IsProj.codRestrict
+-/
 
+#print LinearMap.IsProj.codRestrict_apply /-
 @[simp]
 theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.codRestrict x) = f x :=
   f.codRestrict_apply m x
 #align linear_map.is_proj.cod_restrict_apply LinearMap.IsProj.codRestrict_apply
+-/
 
+#print LinearMap.IsProj.codRestrict_apply_cod /-
 @[simp]
 theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.codRestrict x = x := by
   ext; rw [cod_restrict_apply]; exact h.map_id x x.2
 #align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_cod
+-/
 
+#print LinearMap.IsProj.codRestrict_ker /-
 theorem codRestrict_ker {f : M →ₗ[S] M} (h : IsProj m f) : h.codRestrict.ker = f.ker :=
   f.ker_codRestrict m _
 #align linear_map.is_proj.cod_restrict_ker LinearMap.IsProj.codRestrict_ker
+-/
 
+#print LinearMap.IsProj.isCompl /-
 theorem isCompl {f : E →ₗ[R] E} (h : IsProj p f) : IsCompl p f.ker := by rw [← cod_restrict_ker];
   exact is_compl_of_proj h.cod_restrict_apply_cod
 #align linear_map.is_proj.is_compl LinearMap.IsProj.isCompl
+-/
 
+#print LinearMap.IsProj.eq_conj_prod_map' /-
 theorem eq_conj_prod_map' {f : E →ₗ[R] E} (h : IsProj p f) :
     f =
       (p.prodEquivOfIsCompl f.ker h.IsCompl).toLinearMap ∘ₗ
@@ -459,6 +562,7 @@ theorem eq_conj_prod_map' {f : E →ₗ[R] E} (h : IsProj p f) :
       coe_zero, zero_add, map_coe_ker, prod_equiv_of_is_compl_symm_apply_right, prod_map_apply,
       id_coe, id.def, zero_apply, coe_prod_equiv_of_is_compl']
 #align linear_map.is_proj.eq_conj_prod_map' LinearMap.IsProj.eq_conj_prod_map'
+-/
 
 end IsProj
 
@@ -472,10 +576,12 @@ namespace LinearMap
 
 variable {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E] {p : Submodule R E}
 
+#print LinearMap.IsProj.eq_conj_prodMap /-
 theorem IsProj.eq_conj_prodMap {f : E →ₗ[R] E} (h : IsProj p f) :
     f = (p.prodEquivOfIsCompl f.ker h.IsCompl).conj (prodMap id 0) := by
   rw [LinearEquiv.conj_apply]; exact h.eq_conj_prod_map'
 #align linear_map.is_proj.eq_conj_prod_map LinearMap.IsProj.eq_conj_prodMap
+-/
 
 end LinearMap
 

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

@@ -63,7 +63,7 @@ theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl
   constructor
   · rw [disjoint_iff_inf_le]
     rintro x ⟨hpx, hfx⟩
-    erw [SetLike.mem_coe, mem_ker, hf ⟨x, hpx⟩, mk_eq_zero] at hfx
+    erw [SetLike.mem_coe, mem_ker, hf ⟨x, hpx⟩, mk_eq_zero] at hfx 
     simp only [hfx, SetLike.mem_coe, zero_mem]
   · rw [codisjoint_iff_le_sup]
     intro x hx
@@ -218,7 +218,7 @@ theorem existsUnique_add_of_isCompl_prod (hc : IsCompl p q) (x : E) :
 #align submodule.exists_unique_add_of_is_compl_prod Submodule.existsUnique_add_of_isCompl_prod
 
 theorem existsUnique_add_of_isCompl (hc : IsCompl p q) (x : E) :
-    ∃ (u : p)(v : q), (u : E) + v = x ∧ ∀ (r : p) (s : q), (r : E) + s = x → r = u ∧ s = v :=
+    ∃ (u : p) (v : q), (u : E) + v = x ∧ ∀ (r : p) (s : q), (r : E) + s = x → r = u ∧ s = v :=
   let ⟨u, hu₁, hu₂⟩ := existsUnique_add_of_isCompl_prod hc x
   ⟨u.1, u.2, hu₁, fun r s hrs => Prod.eq_iff_fst_eq_snd_eq.1 (hu₂ ⟨r, s⟩ hrs)⟩
 #align submodule.exists_unique_add_of_is_compl Submodule.existsUnique_add_of_isCompl

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

@@ -47,9 +47,6 @@ variable {p}
 
 open Submodule
 
-/- warning: linear_map.ker_id_sub_eq_of_proj -> LinearMap.ker_id_sub_eq_of_proj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ker_id_sub_eq_of_proj LinearMap.ker_id_sub_eq_of_projₓ'. -/
 theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
     ker (id - p.Subtype.comp f) = p := by
   ext x
@@ -57,16 +54,10 @@ theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
   exact ⟨fun h => h.symm ▸ Submodule.coe_mem _, fun hx => by erw [hf ⟨x, hx⟩, Subtype.coe_mk]⟩
 #align linear_map.ker_id_sub_eq_of_proj LinearMap.ker_id_sub_eq_of_proj
 
-/- warning: linear_map.range_eq_of_proj -> LinearMap.range_eq_of_proj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.range_eq_of_proj LinearMap.range_eq_of_projₓ'. -/
 theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f = ⊤ :=
   range_eq_top.2 fun x => ⟨x, hf x⟩
 #align linear_map.range_eq_of_proj LinearMap.range_eq_of_proj
 
-/- warning: linear_map.is_compl_of_proj -> LinearMap.isCompl_of_proj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_compl_of_proj LinearMap.isCompl_of_projₓ'. -/
 theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl p f.ker :=
   by
   constructor
@@ -87,12 +78,6 @@ namespace Submodule
 
 open LinearMap
 
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-Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl Submodule.quotientEquivOfIsComplₓ'. -/
 /-- If `q` is a complement of `p`, then `M/p ≃ q`. -/
 def quotientEquivOfIsCompl (h : IsCompl p q) : (E ⧸ p) ≃ₗ[R] q :=
   LinearEquiv.symm <|
@@ -101,36 +86,24 @@ def quotientEquivOfIsCompl (h : IsCompl p q) : (E ⧸ p) ≃ₗ[R] q :=
         rw [← range_eq_top, range_comp, range_subtype, map_mkq_eq_top, h.sup_eq_top]⟩
 #align submodule.quotient_equiv_of_is_compl Submodule.quotientEquivOfIsCompl
 
-/- warning: submodule.quotient_equiv_of_is_compl_symm_apply -> Submodule.quotientEquivOfIsCompl_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl_symm_apply Submodule.quotientEquivOfIsCompl_symm_applyₓ'. -/
 @[simp]
 theorem quotientEquivOfIsCompl_symm_apply (h : IsCompl p q) (x : q) :
     (quotientEquivOfIsCompl p q h).symm x = Quotient.mk x :=
   rfl
 #align submodule.quotient_equiv_of_is_compl_symm_apply Submodule.quotientEquivOfIsCompl_symm_apply
 
-/- warning: submodule.quotient_equiv_of_is_compl_apply_mk_coe -> Submodule.quotientEquivOfIsCompl_apply_mk_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl_apply_mk_coe Submodule.quotientEquivOfIsCompl_apply_mk_coeₓ'. -/
 @[simp]
 theorem quotientEquivOfIsCompl_apply_mk_coe (h : IsCompl p q) (x : q) :
     quotientEquivOfIsCompl p q h (Quotient.mk x) = x :=
   (quotientEquivOfIsCompl p q h).apply_symm_apply x
 #align submodule.quotient_equiv_of_is_compl_apply_mk_coe Submodule.quotientEquivOfIsCompl_apply_mk_coe
 
-/- warning: submodule.mk_quotient_equiv_of_is_compl_apply -> Submodule.mk_quotientEquivOfIsCompl_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mk_quotient_equiv_of_is_compl_apply Submodule.mk_quotientEquivOfIsCompl_applyₓ'. -/
 @[simp]
 theorem mk_quotientEquivOfIsCompl_apply (h : IsCompl p q) (x : E ⧸ p) :
     (Quotient.mk (quotientEquivOfIsCompl p q h x) : E ⧸ p) = x :=
   (quotientEquivOfIsCompl p q h).symm_apply_apply x
 #align submodule.mk_quotient_equiv_of_is_compl_apply Submodule.mk_quotientEquivOfIsCompl_apply
 
-/- warning: submodule.prod_equiv_of_is_compl -> Submodule.prodEquivOfIsCompl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl Submodule.prodEquivOfIsComplₓ'. -/
 /-- If `q` is a complement of `p`, then `p × q` is isomorphic to `E`. It is the unique
 linear map `f : E → p` such that `f x = x` for `x ∈ p` and `f x = 0` for `x ∈ q`. -/
 def prodEquivOfIsCompl (h : IsCompl p q) : (p × q) ≃ₗ[R] E :=
@@ -143,45 +116,30 @@ def prodEquivOfIsCompl (h : IsCompl p q) : (p × q) ≃ₗ[R] E :=
   · rw [← range_eq_top, ← sup_eq_range, h.sup_eq_top]
 #align submodule.prod_equiv_of_is_compl Submodule.prodEquivOfIsCompl
 
-/- warning: submodule.coe_prod_equiv_of_is_compl -> Submodule.coe_prodEquivOfIsCompl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.coe_prod_equiv_of_is_compl Submodule.coe_prodEquivOfIsComplₓ'. -/
 @[simp]
 theorem coe_prodEquivOfIsCompl (h : IsCompl p q) :
     (prodEquivOfIsCompl p q h : p × q →ₗ[R] E) = p.Subtype.coprod q.Subtype :=
   rfl
 #align submodule.coe_prod_equiv_of_is_compl Submodule.coe_prodEquivOfIsCompl
 
-/- warning: submodule.coe_prod_equiv_of_is_compl' -> Submodule.coe_prodEquivOfIsCompl' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.coe_prod_equiv_of_is_compl' Submodule.coe_prodEquivOfIsCompl'ₓ'. -/
 @[simp]
 theorem coe_prodEquivOfIsCompl' (h : IsCompl p q) (x : p × q) :
     prodEquivOfIsCompl p q h x = x.1 + x.2 :=
   rfl
 #align submodule.coe_prod_equiv_of_is_compl' Submodule.coe_prodEquivOfIsCompl'
 
-/- warning: submodule.prod_equiv_of_is_compl_symm_apply_left -> Submodule.prodEquivOfIsCompl_symm_apply_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_left Submodule.prodEquivOfIsCompl_symm_apply_leftₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_left (h : IsCompl p q) (x : p) :
     (prodEquivOfIsCompl p q h).symm x = (x, 0) :=
   (prodEquivOfIsCompl p q h).symm_apply_eq.2 <| by simp
 #align submodule.prod_equiv_of_is_compl_symm_apply_left Submodule.prodEquivOfIsCompl_symm_apply_left
 
-/- warning: submodule.prod_equiv_of_is_compl_symm_apply_right -> Submodule.prodEquivOfIsCompl_symm_apply_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_right Submodule.prodEquivOfIsCompl_symm_apply_rightₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_right (h : IsCompl p q) (x : q) :
     (prodEquivOfIsCompl p q h).symm x = (0, x) :=
   (prodEquivOfIsCompl p q h).symm_apply_eq.2 <| by simp
 #align submodule.prod_equiv_of_is_compl_symm_apply_right Submodule.prodEquivOfIsCompl_symm_apply_right
 
-/- warning: submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero -> Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zeroₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
     ((prodEquivOfIsCompl p q h).symm x).1 = 0 ↔ x ∈ q :=
@@ -191,9 +149,6 @@ theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
     mem_right_iff_eq_zero_of_disjoint h.disjoint]
 #align submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero
 
-/- warning: submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero -> Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zeroₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_snd_eq_zero (h : IsCompl p q) {x : E} :
     ((prodEquivOfIsCompl p q h).symm x).2 = 0 ↔ x ∈ p :=
@@ -203,21 +158,12 @@ theorem prodEquivOfIsCompl_symm_apply_snd_eq_zero (h : IsCompl p q) {x : E} :
     mem_left_iff_eq_zero_of_disjoint h.disjoint]
 #align submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero
 
-/- warning: submodule.prod_comm_trans_prod_equiv_of_is_compl -> Submodule.prodComm_trans_prodEquivOfIsCompl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.prod_comm_trans_prod_equiv_of_is_compl Submodule.prodComm_trans_prodEquivOfIsComplₓ'. -/
 @[simp]
 theorem prodComm_trans_prodEquivOfIsCompl (h : IsCompl p q) :
     LinearEquiv.prodComm R q p ≪≫ₗ prodEquivOfIsCompl p q h = prodEquivOfIsCompl q p h.symm :=
   LinearEquiv.ext fun _ => add_comm _ _
 #align submodule.prod_comm_trans_prod_equiv_of_is_compl Submodule.prodComm_trans_prodEquivOfIsCompl
 
-/- warning: submodule.linear_proj_of_is_compl -> Submodule.linearProjOfIsCompl is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl Submodule.linearProjOfIsComplₓ'. -/
 /-- Projection to a submodule along its complement. -/
 def linearProjOfIsCompl (h : IsCompl p q) : E →ₗ[R] p :=
   LinearMap.fst R p q ∘ₗ ↑(prodEquivOfIsCompl p q h).symm
@@ -225,91 +171,58 @@ def linearProjOfIsCompl (h : IsCompl p q) : E →ₗ[R] p :=
 
 variable {p q}
 
-/- warning: submodule.linear_proj_of_is_compl_apply_left -> Submodule.linearProjOfIsCompl_apply_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_left Submodule.linearProjOfIsCompl_apply_leftₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_left (h : IsCompl p q) (x : p) :
     linearProjOfIsCompl p q h x = x := by simp [linear_proj_of_is_compl]
 #align submodule.linear_proj_of_is_compl_apply_left Submodule.linearProjOfIsCompl_apply_left
 
-/- warning: submodule.linear_proj_of_is_compl_range -> Submodule.linearProjOfIsCompl_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_range Submodule.linearProjOfIsCompl_rangeₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_range (h : IsCompl p q) : (linearProjOfIsCompl p q h).range = ⊤ :=
   range_eq_of_proj (linearProjOfIsCompl_apply_left h)
 #align submodule.linear_proj_of_is_compl_range Submodule.linearProjOfIsCompl_range
 
-/- warning: submodule.linear_proj_of_is_compl_apply_eq_zero_iff -> Submodule.linearProjOfIsCompl_apply_eq_zero_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_eq_zero_iff Submodule.linearProjOfIsCompl_apply_eq_zero_iffₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
     linearProjOfIsCompl p q h x = 0 ↔ x ∈ q := by simp [linear_proj_of_is_compl]
 #align submodule.linear_proj_of_is_compl_apply_eq_zero_iff Submodule.linearProjOfIsCompl_apply_eq_zero_iff
 
-/- warning: submodule.linear_proj_of_is_compl_apply_right' -> Submodule.linearProjOfIsCompl_apply_right' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right' Submodule.linearProjOfIsCompl_apply_right'ₓ'. -/
 theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q) :
     linearProjOfIsCompl p q h x = 0 :=
   (linearProjOfIsCompl_apply_eq_zero_iff h).2 hx
 #align submodule.linear_proj_of_is_compl_apply_right' Submodule.linearProjOfIsCompl_apply_right'
 
-/- warning: submodule.linear_proj_of_is_compl_apply_right -> Submodule.linearProjOfIsCompl_apply_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right Submodule.linearProjOfIsCompl_apply_rightₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_right (h : IsCompl p q) (x : q) :
     linearProjOfIsCompl p q h x = 0 :=
   linearProjOfIsCompl_apply_right' h x x.2
 #align submodule.linear_proj_of_is_compl_apply_right Submodule.linearProjOfIsCompl_apply_right
 
-/- warning: submodule.linear_proj_of_is_compl_ker -> Submodule.linearProjOfIsCompl_ker is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_ker Submodule.linearProjOfIsCompl_kerₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_ker (h : IsCompl p q) : (linearProjOfIsCompl p q h).ker = q :=
   ext fun x => mem_ker.trans (linearProjOfIsCompl_apply_eq_zero_iff h)
 #align submodule.linear_proj_of_is_compl_ker Submodule.linearProjOfIsCompl_ker
 
-/- warning: submodule.linear_proj_of_is_compl_comp_subtype -> Submodule.linearProjOfIsCompl_comp_subtype is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_comp_subtype Submodule.linearProjOfIsCompl_comp_subtypeₓ'. -/
 theorem linearProjOfIsCompl_comp_subtype (h : IsCompl p q) :
     (linearProjOfIsCompl p q h).comp p.Subtype = id :=
   LinearMap.ext <| linearProjOfIsCompl_apply_left h
 #align submodule.linear_proj_of_is_compl_comp_subtype Submodule.linearProjOfIsCompl_comp_subtype
 
-/- warning: submodule.linear_proj_of_is_compl_idempotent -> Submodule.linearProjOfIsCompl_idempotent is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_idempotent Submodule.linearProjOfIsCompl_idempotentₓ'. -/
 theorem linearProjOfIsCompl_idempotent (h : IsCompl p q) (x : E) :
     linearProjOfIsCompl p q h (linearProjOfIsCompl p q h x) = linearProjOfIsCompl p q h x :=
   linearProjOfIsCompl_apply_left h _
 #align submodule.linear_proj_of_is_compl_idempotent Submodule.linearProjOfIsCompl_idempotent
 
-/- warning: submodule.exists_unique_add_of_is_compl_prod -> Submodule.existsUnique_add_of_isCompl_prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.exists_unique_add_of_is_compl_prod Submodule.existsUnique_add_of_isCompl_prodₓ'. -/
 theorem existsUnique_add_of_isCompl_prod (hc : IsCompl p q) (x : E) :
     ∃! u : p × q, (u.fst : E) + u.snd = x :=
   (prodEquivOfIsCompl _ _ hc).toEquiv.Bijective.ExistsUnique _
 #align submodule.exists_unique_add_of_is_compl_prod Submodule.existsUnique_add_of_isCompl_prod
 
-/- warning: submodule.exists_unique_add_of_is_compl -> Submodule.existsUnique_add_of_isCompl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.exists_unique_add_of_is_compl Submodule.existsUnique_add_of_isComplₓ'. -/
 theorem existsUnique_add_of_isCompl (hc : IsCompl p q) (x : E) :
     ∃ (u : p)(v : q), (u : E) + v = x ∧ ∀ (r : p) (s : q), (r : E) + s = x → r = u ∧ s = v :=
   let ⟨u, hu₁, hu₂⟩ := existsUnique_add_of_isCompl_prod hc x
   ⟨u.1, u.2, hu₁, fun r s hrs => Prod.eq_iff_fst_eq_snd_eq.1 (hu₂ ⟨r, s⟩ hrs)⟩
 #align submodule.exists_unique_add_of_is_compl Submodule.existsUnique_add_of_isCompl
 
-/- warning: submodule.linear_proj_add_linear_proj_of_is_compl_eq_self -> Submodule.linear_proj_add_linearProjOfIsCompl_eq_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_add_linear_proj_of_is_compl_eq_self Submodule.linear_proj_add_linearProjOfIsCompl_eq_selfₓ'. -/
 theorem linear_proj_add_linearProjOfIsCompl_eq_self (hpq : IsCompl p q) (x : E) :
     (p.linearProjOfIsCompl q hpq x + q.linearProjOfIsCompl p hpq.symm x : E) = x :=
   by
@@ -324,9 +237,6 @@ namespace LinearMap
 
 open Submodule
 
-/- warning: linear_map.of_is_compl -> LinearMap.ofIsCompl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl LinearMap.ofIsComplₓ'. -/
 /-- Given linear maps `φ` and `ψ` from complement submodules, `of_is_compl` is
 the induced linear map over the entire module. -/
 def ofIsCompl {p q : Submodule R E} (h : IsCompl p q) (φ : p →ₗ[R] F) (ψ : q →ₗ[R] F) : E →ₗ[R] F :=
@@ -335,25 +245,16 @@ def ofIsCompl {p q : Submodule R E} (h : IsCompl p q) (φ : p →ₗ[R] F) (ψ :
 
 variable {p q}
 
-/- warning: linear_map.of_is_compl_left_apply -> LinearMap.ofIsCompl_left_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_left_apply LinearMap.ofIsCompl_left_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (u : p) :
     ofIsCompl h φ ψ (u : E) = φ u := by simp [of_is_compl]
 #align linear_map.of_is_compl_left_apply LinearMap.ofIsCompl_left_apply
 
-/- warning: linear_map.of_is_compl_right_apply -> LinearMap.ofIsCompl_right_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_right_apply LinearMap.ofIsCompl_right_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (v : q) :
     ofIsCompl h φ ψ (v : E) = ψ v := by simp [of_is_compl]
 #align linear_map.of_is_compl_right_apply LinearMap.ofIsCompl_right_apply
 
-/- warning: linear_map.of_is_compl_eq -> LinearMap.ofIsCompl_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_eq LinearMap.ofIsCompl_eqₓ'. -/
 theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : ∀ u, φ u = χ u) (hψ : ∀ u, ψ u = χ u) : ofIsCompl h φ ψ = χ :=
   by
@@ -362,34 +263,22 @@ theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F}
   simp [of_is_compl, hφ, hψ]
 #align linear_map.of_is_compl_eq LinearMap.ofIsCompl_eq
 
-/- warning: linear_map.of_is_compl_eq' -> LinearMap.ofIsCompl_eq' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_eq' LinearMap.ofIsCompl_eq'ₓ'. -/
 theorem ofIsCompl_eq' (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : φ = χ.comp p.Subtype) (hψ : ψ = χ.comp q.Subtype) : ofIsCompl h φ ψ = χ :=
   ofIsCompl_eq h (fun _ => hφ.symm ▸ rfl) fun _ => hψ.symm ▸ rfl
 #align linear_map.of_is_compl_eq' LinearMap.ofIsCompl_eq'
 
-/- warning: linear_map.of_is_compl_zero -> LinearMap.ofIsCompl_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_zero LinearMap.ofIsCompl_zeroₓ'. -/
 @[simp]
 theorem ofIsCompl_zero (h : IsCompl p q) : (ofIsCompl h 0 0 : E →ₗ[R] F) = 0 :=
   ofIsCompl_eq _ (fun _ => rfl) fun _ => rfl
 #align linear_map.of_is_compl_zero LinearMap.ofIsCompl_zero
 
-/- warning: linear_map.of_is_compl_add -> LinearMap.ofIsCompl_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_add LinearMap.ofIsCompl_addₓ'. -/
 @[simp]
 theorem ofIsCompl_add (h : IsCompl p q) {φ₁ φ₂ : p →ₗ[R] F} {ψ₁ ψ₂ : q →ₗ[R] F} :
     ofIsCompl h (φ₁ + φ₂) (ψ₁ + ψ₂) = ofIsCompl h φ₁ ψ₁ + ofIsCompl h φ₂ ψ₂ :=
   ofIsCompl_eq _ (by simp) (by simp)
 #align linear_map.of_is_compl_add LinearMap.ofIsCompl_add
 
-/- warning: linear_map.of_is_compl_smul -> LinearMap.ofIsCompl_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_smul LinearMap.ofIsCompl_smulₓ'. -/
 @[simp]
 theorem ofIsCompl_smul {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E]
     {F : Type _} [AddCommGroup F] [Module R F] {p q : Submodule R E} (h : IsCompl p q)
@@ -401,9 +290,6 @@ section
 
 variable {R₁ : Type _} [CommRing R₁] [Module R₁ E] [Module R₁ F]
 
-/- warning: linear_map.of_is_compl_prod -> LinearMap.ofIsComplProd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod LinearMap.ofIsComplProdₓ'. -/
 /-- The linear map from `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` to `E →ₗ[R₁] F`. -/
 def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
     (p →ₗ[R₁] F) × (q →ₗ[R₁] F) →ₗ[R₁] E →ₗ[R₁] F
@@ -413,18 +299,12 @@ def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
   map_smul' := by intro c φ; simp [Prod.smul_snd, Prod.smul_fst, of_is_compl_smul]
 #align linear_map.of_is_compl_prod LinearMap.ofIsComplProd
 
-/- warning: linear_map.of_is_compl_prod_apply -> LinearMap.ofIsComplProd_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_applyₓ'. -/
 @[simp]
 theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
     (φ : (p →ₗ[R₁] F) × (q →ₗ[R₁] F)) : ofIsComplProd h φ = ofIsCompl h φ.1 φ.2 :=
   rfl
 #align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_apply
 
-/- warning: linear_map.of_is_compl_prod_equiv -> LinearMap.ofIsComplProdEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_equiv LinearMap.ofIsComplProdEquivₓ'. -/
 /-- The natural linear equivalence between `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` and `E →ₗ[R₁] F`. -/
 def ofIsComplProdEquiv {p q : Submodule R₁ E} (h : IsCompl p q) :
     ((p →ₗ[R₁] F) × (q →ₗ[R₁] F)) ≃ₗ[R₁] E →ₗ[R₁] F :=
@@ -442,9 +322,6 @@ def ofIsComplProdEquiv {p q : Submodule R₁ E} (h : IsCompl p q) :
 
 end
 
-/- warning: linear_map.linear_proj_of_is_compl_of_proj -> LinearMap.linearProjOfIsCompl_of_proj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.linear_proj_of_is_compl_of_proj LinearMap.linearProjOfIsCompl_of_projₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x) :
     p.linearProjOfIsCompl f.ker (isCompl_of_proj hf) = f :=
@@ -455,9 +332,6 @@ theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x
   simp [hf]
 #align linear_map.linear_proj_of_is_compl_of_proj LinearMap.linearProjOfIsCompl_of_proj
 
-/- warning: linear_map.equiv_prod_of_surjective_of_is_compl -> LinearMap.equivProdOfSurjectiveOfIsCompl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.equiv_prod_of_surjective_of_is_compl LinearMap.equivProdOfSurjectiveOfIsComplₓ'. -/
 /-- If `f : E →ₗ[R] F` and `g : E →ₗ[R] G` are two surjective linear maps and
 their kernels are complement of each other, then `x ↦ (f x, g x)` defines
 a linear equivalence `E ≃ₗ[R] F × G`. -/
@@ -468,9 +342,6 @@ def equivProdOfSurjectiveOfIsCompl (f : E →ₗ[R] F) (g : E →ₗ[R] G) (hf :
       simp [range_prod_eq hfg.sup_eq_top, *]⟩
 #align linear_map.equiv_prod_of_surjective_of_is_compl LinearMap.equivProdOfSurjectiveOfIsCompl
 
-/- warning: linear_map.coe_equiv_prod_of_surjective_of_is_compl -> LinearMap.coe_equivProdOfSurjectiveOfIsCompl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.coe_equiv_prod_of_surjective_of_is_compl LinearMap.coe_equivProdOfSurjectiveOfIsComplₓ'. -/
 @[simp]
 theorem coe_equivProdOfSurjectiveOfIsCompl {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
     (hg : g.range = ⊤) (hfg : IsCompl f.ker g.ker) :
@@ -478,9 +349,6 @@ theorem coe_equivProdOfSurjectiveOfIsCompl {f : E →ₗ[R] F} {g : E →ₗ[R]
   rfl
 #align linear_map.coe_equiv_prod_of_surjective_of_is_compl LinearMap.coe_equivProdOfSurjectiveOfIsCompl
 
-/- warning: linear_map.equiv_prod_of_surjective_of_is_compl_apply -> LinearMap.equivProdOfSurjectiveOfIsCompl_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.equiv_prod_of_surjective_of_is_compl_apply LinearMap.equivProdOfSurjectiveOfIsCompl_applyₓ'. -/
 @[simp]
 theorem equivProdOfSurjectiveOfIsCompl_apply {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
     (hg : g.range = ⊤) (hfg : IsCompl f.ker g.ker) (x : E) :
@@ -494,9 +362,6 @@ namespace Submodule
 
 open LinearMap
 
-/- warning: submodule.is_compl_equiv_proj -> Submodule.isComplEquivProj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.is_compl_equiv_proj Submodule.isComplEquivProjₓ'. -/
 /-- Equivalence between submodules `q` such that `is_compl p q` and linear maps `f : E →ₗ[R] p`
 such that `∀ x : p, f x = x`. -/
 def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p, f x = x }
@@ -507,18 +372,12 @@ def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p
   right_inv := fun ⟨f, hf⟩ => Subtype.eq <| f.linearProjOfIsCompl_of_proj hf
 #align submodule.is_compl_equiv_proj Submodule.isComplEquivProj
 
-/- warning: submodule.coe_is_compl_equiv_proj_apply -> Submodule.coe_isComplEquivProj_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
     (p.isComplEquivProj q : E →ₗ[R] p) = linearProjOfIsCompl p q q.2 :=
   rfl
 #align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_apply
 
-/- warning: submodule.coe_is_compl_equiv_proj_symm_apply -> Submodule.coe_isComplEquivProj_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_symm_apply Submodule.coe_isComplEquivProj_symm_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_symm_apply (f : { f : E →ₗ[R] p // ∀ x : p, f x = x }) :
     (p.isComplEquivProj.symm f : Submodule R E) = (f : E →ₗ[R] p).ker :=
@@ -544,9 +403,6 @@ structure IsProj {F : Type _} [FunLike F M fun _ => M] (f : F) : Prop where
 #align linear_map.is_proj LinearMap.IsProj
 -/
 
-/- warning: linear_map.is_proj_iff_idempotent -> LinearMap.isProj_iff_idempotent is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_proj_iff_idempotent LinearMap.isProj_iff_idempotentₓ'. -/
 theorem isProj_iff_idempotent (f : M →ₗ[S] M) : (∃ p : Submodule S M, IsProj p f) ↔ f ∘ₗ f = f :=
   by
   constructor
@@ -560,9 +416,6 @@ namespace IsProj
 
 variable {p m}
 
-/- warning: linear_map.is_proj.cod_restrict -> LinearMap.IsProj.codRestrict is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict LinearMap.IsProj.codRestrictₓ'. -/
 /-- Restriction of the codomain of a projection of onto a subspace `p` to `p` instead of the whole
 space.
 -/
@@ -570,39 +423,24 @@ def codRestrict {f : M →ₗ[S] M} (h : IsProj m f) : M →ₗ[S] m :=
   f.codRestrict m h.map_mem
 #align linear_map.is_proj.cod_restrict LinearMap.IsProj.codRestrict
 
-/- warning: linear_map.is_proj.cod_restrict_apply -> LinearMap.IsProj.codRestrict_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply LinearMap.IsProj.codRestrict_applyₓ'. -/
 @[simp]
 theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.codRestrict x) = f x :=
   f.codRestrict_apply m x
 #align linear_map.is_proj.cod_restrict_apply LinearMap.IsProj.codRestrict_apply
 
-/- warning: linear_map.is_proj.cod_restrict_apply_cod -> LinearMap.IsProj.codRestrict_apply_cod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_codₓ'. -/
 @[simp]
 theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.codRestrict x = x := by
   ext; rw [cod_restrict_apply]; exact h.map_id x x.2
 #align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_cod
 
-/- warning: linear_map.is_proj.cod_restrict_ker -> LinearMap.IsProj.codRestrict_ker is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_ker LinearMap.IsProj.codRestrict_kerₓ'. -/
 theorem codRestrict_ker {f : M →ₗ[S] M} (h : IsProj m f) : h.codRestrict.ker = f.ker :=
   f.ker_codRestrict m _
 #align linear_map.is_proj.cod_restrict_ker LinearMap.IsProj.codRestrict_ker
 
-/- warning: linear_map.is_proj.is_compl -> LinearMap.IsProj.isCompl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.is_compl LinearMap.IsProj.isComplₓ'. -/
 theorem isCompl {f : E →ₗ[R] E} (h : IsProj p f) : IsCompl p f.ker := by rw [← cod_restrict_ker];
   exact is_compl_of_proj h.cod_restrict_apply_cod
 #align linear_map.is_proj.is_compl LinearMap.IsProj.isCompl
 
-/- warning: linear_map.is_proj.eq_conj_prod_map' -> LinearMap.IsProj.eq_conj_prod_map' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map' LinearMap.IsProj.eq_conj_prod_map'ₓ'. -/
 theorem eq_conj_prod_map' {f : E →ₗ[R] E} (h : IsProj p f) :
     f =
       (p.prodEquivOfIsCompl f.ker h.IsCompl).toLinearMap ∘ₗ
@@ -634,9 +472,6 @@ namespace LinearMap
 
 variable {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E] {p : Submodule R E}
 
-/- warning: linear_map.is_proj.eq_conj_prod_map -> LinearMap.IsProj.eq_conj_prodMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map LinearMap.IsProj.eq_conj_prodMapₓ'. -/
 theorem IsProj.eq_conj_prodMap {f : E →ₗ[R] E} (h : IsProj p f) :
     f = (p.prodEquivOfIsCompl f.ker h.IsCompl).conj (prodMap id 0) := by
   rw [LinearEquiv.conj_apply]; exact h.eq_conj_prod_map'

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

@@ -409,12 +409,8 @@ def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
     (p →ₗ[R₁] F) × (q →ₗ[R₁] F) →ₗ[R₁] E →ₗ[R₁] F
     where
   toFun φ := ofIsCompl h φ.1 φ.2
-  map_add' := by
-    intro φ ψ
-    rw [Prod.snd_add, Prod.fst_add, of_is_compl_add]
-  map_smul' := by
-    intro c φ
-    simp [Prod.smul_snd, Prod.smul_fst, of_is_compl_smul]
+  map_add' := by intro φ ψ; rw [Prod.snd_add, Prod.fst_add, of_is_compl_add]
+  map_smul' := by intro c φ; simp [Prod.smul_snd, Prod.smul_fst, of_is_compl_smul]
 #align linear_map.of_is_compl_prod LinearMap.ofIsComplProd
 
 /- warning: linear_map.of_is_compl_prod_apply -> LinearMap.ofIsComplProd_apply is a dubious translation:
@@ -468,9 +464,7 @@ a linear equivalence `E ≃ₗ[R] F × G`. -/
 def equivProdOfSurjectiveOfIsCompl (f : E →ₗ[R] F) (g : E →ₗ[R] G) (hf : f.range = ⊤)
     (hg : g.range = ⊤) (hfg : IsCompl f.ker g.ker) : E ≃ₗ[R] F × G :=
   LinearEquiv.ofBijective (f.Prod g)
-    ⟨by simp [← ker_eq_bot, hfg.inf_eq_bot],
-      by
-      rw [← range_eq_top]
+    ⟨by simp [← ker_eq_bot, hfg.inf_eq_bot], by rw [← range_eq_top];
       simp [range_prod_eq hfg.sup_eq_top, *]⟩
 #align linear_map.equiv_prod_of_surjective_of_is_compl LinearMap.equivProdOfSurjectiveOfIsCompl
 
@@ -556,19 +550,10 @@ Case conversion may be inaccurate. Consider using '#align linear_map.is_proj_iff
 theorem isProj_iff_idempotent (f : M →ₗ[S] M) : (∃ p : Submodule S M, IsProj p f) ↔ f ∘ₗ f = f :=
   by
   constructor
-  · intro h
-    obtain ⟨p, hp⟩ := h
-    ext
-    rw [comp_apply]
-    exact hp.map_id (f x) (hp.map_mem x)
-  · intro h
-    use f.range
-    constructor
-    · intro x
-      exact mem_range_self f x
-    · intro x hx
-      obtain ⟨y, hy⟩ := mem_range.1 hx
-      rw [← hy, ← comp_apply, h]
+  · intro h; obtain ⟨p, hp⟩ := h; ext; rw [comp_apply]; exact hp.map_id (f x) (hp.map_mem x)
+  · intro h; use f.range; constructor
+    · intro x; exact mem_range_self f x
+    · intro x hx; obtain ⟨y, hy⟩ := mem_range.1 hx; rw [← hy, ← comp_apply, h]
 #align linear_map.is_proj_iff_idempotent LinearMap.isProj_iff_idempotent
 
 namespace IsProj
@@ -597,11 +582,8 @@ theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.c
 <too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_codₓ'. -/
 @[simp]
-theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.codRestrict x = x :=
-  by
-  ext
-  rw [cod_restrict_apply]
-  exact h.map_id x x.2
+theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.codRestrict x = x := by
+  ext; rw [cod_restrict_apply]; exact h.map_id x x.2
 #align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_cod
 
 /- warning: linear_map.is_proj.cod_restrict_ker -> LinearMap.IsProj.codRestrict_ker is a dubious translation:
@@ -614,9 +596,7 @@ theorem codRestrict_ker {f : M →ₗ[S] M} (h : IsProj m f) : h.codRestrict.ker
 /- warning: linear_map.is_proj.is_compl -> LinearMap.IsProj.isCompl is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.is_compl LinearMap.IsProj.isComplₓ'. -/
-theorem isCompl {f : E →ₗ[R] E} (h : IsProj p f) : IsCompl p f.ker :=
-  by
-  rw [← cod_restrict_ker]
+theorem isCompl {f : E →ₗ[R] E} (h : IsProj p f) : IsCompl p f.ker := by rw [← cod_restrict_ker];
   exact is_compl_of_proj h.cod_restrict_apply_cod
 #align linear_map.is_proj.is_compl LinearMap.IsProj.isCompl
 
@@ -658,10 +638,8 @@ variable {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E] {p
 <too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map LinearMap.IsProj.eq_conj_prodMapₓ'. -/
 theorem IsProj.eq_conj_prodMap {f : E →ₗ[R] E} (h : IsProj p f) :
-    f = (p.prodEquivOfIsCompl f.ker h.IsCompl).conj (prodMap id 0) :=
-  by
-  rw [LinearEquiv.conj_apply]
-  exact h.eq_conj_prod_map'
+    f = (p.prodEquivOfIsCompl f.ker h.IsCompl).conj (prodMap id 0) := by
+  rw [LinearEquiv.conj_apply]; exact h.eq_conj_prod_map'
 #align linear_map.is_proj.eq_conj_prod_map LinearMap.IsProj.eq_conj_prodMap
 
 end LinearMap

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

@@ -48,10 +48,7 @@ variable {p}
 open Submodule
 
 /- warning: linear_map.ker_id_sub_eq_of_proj -> LinearMap.ker_id_sub_eq_of_proj is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.ker_id_sub_eq_of_proj LinearMap.ker_id_sub_eq_of_projₓ'. -/
 theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
     ker (id - p.Subtype.comp f) = p := by
@@ -61,20 +58,14 @@ theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
 #align linear_map.ker_id_sub_eq_of_proj LinearMap.ker_id_sub_eq_of_proj
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.range_eq_of_proj LinearMap.range_eq_of_projₓ'. -/
 theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f = ⊤ :=
   range_eq_top.2 fun x => ⟨x, hf x⟩
 #align linear_map.range_eq_of_proj LinearMap.range_eq_of_proj
 
 /- warning: linear_map.is_compl_of_proj -> LinearMap.isCompl_of_proj is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_compl_of_proj LinearMap.isCompl_of_projₓ'. -/
 theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl p f.ker :=
   by
@@ -111,10 +102,7 @@ def quotientEquivOfIsCompl (h : IsCompl p q) : (E ⧸ p) ≃ₗ[R] q :=
 #align submodule.quotient_equiv_of_is_compl Submodule.quotientEquivOfIsCompl
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl_symm_apply Submodule.quotientEquivOfIsCompl_symm_applyₓ'. -/
 @[simp]
 theorem quotientEquivOfIsCompl_symm_apply (h : IsCompl p q) (x : q) :
@@ -123,10 +111,7 @@ theorem quotientEquivOfIsCompl_symm_apply (h : IsCompl p q) (x : q) :
 #align submodule.quotient_equiv_of_is_compl_symm_apply Submodule.quotientEquivOfIsCompl_symm_apply
 
 /- warning: submodule.quotient_equiv_of_is_compl_apply_mk_coe -> Submodule.quotientEquivOfIsCompl_apply_mk_coe is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl_apply_mk_coe Submodule.quotientEquivOfIsCompl_apply_mk_coeₓ'. -/
 @[simp]
 theorem quotientEquivOfIsCompl_apply_mk_coe (h : IsCompl p q) (x : q) :
@@ -135,10 +120,7 @@ theorem quotientEquivOfIsCompl_apply_mk_coe (h : IsCompl p q) (x : q) :
 #align submodule.quotient_equiv_of_is_compl_apply_mk_coe Submodule.quotientEquivOfIsCompl_apply_mk_coe
 
 /- warning: submodule.mk_quotient_equiv_of_is_compl_apply -> Submodule.mk_quotientEquivOfIsCompl_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mk_quotient_equiv_of_is_compl_apply Submodule.mk_quotientEquivOfIsCompl_applyₓ'. -/
 @[simp]
 theorem mk_quotientEquivOfIsCompl_apply (h : IsCompl p q) (x : E ⧸ p) :
@@ -147,10 +129,7 @@ theorem mk_quotientEquivOfIsCompl_apply (h : IsCompl p q) (x : E ⧸ p) :
 #align submodule.mk_quotient_equiv_of_is_compl_apply Submodule.mk_quotientEquivOfIsCompl_apply
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl Submodule.prodEquivOfIsComplₓ'. -/
 /-- If `q` is a complement of `p`, then `p × q` is isomorphic to `E`. It is the unique
 linear map `f : E → p` such that `f x = x` for `x ∈ p` and `f x = 0` for `x ∈ q`. -/
@@ -165,10 +144,7 @@ def prodEquivOfIsCompl (h : IsCompl p q) : (p × q) ≃ₗ[R] E :=
 #align submodule.prod_equiv_of_is_compl Submodule.prodEquivOfIsCompl
 
 /- warning: submodule.coe_prod_equiv_of_is_compl -> Submodule.coe_prodEquivOfIsCompl is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align submodule.coe_prod_equiv_of_is_compl Submodule.coe_prodEquivOfIsComplₓ'. -/
 @[simp]
 theorem coe_prodEquivOfIsCompl (h : IsCompl p q) :
@@ -177,10 +153,7 @@ theorem coe_prodEquivOfIsCompl (h : IsCompl p q) :
 #align submodule.coe_prod_equiv_of_is_compl Submodule.coe_prodEquivOfIsCompl
 
 /- warning: submodule.coe_prod_equiv_of_is_compl' -> Submodule.coe_prodEquivOfIsCompl' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.coe_prod_equiv_of_is_compl' Submodule.coe_prodEquivOfIsCompl'ₓ'. -/
 @[simp]
 theorem coe_prodEquivOfIsCompl' (h : IsCompl p q) (x : p × q) :
@@ -189,10 +162,7 @@ theorem coe_prodEquivOfIsCompl' (h : IsCompl p q) (x : p × q) :
 #align submodule.coe_prod_equiv_of_is_compl' Submodule.coe_prodEquivOfIsCompl'
 
 /- warning: submodule.prod_equiv_of_is_compl_symm_apply_left -> Submodule.prodEquivOfIsCompl_symm_apply_left is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_left Submodule.prodEquivOfIsCompl_symm_apply_leftₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_left (h : IsCompl p q) (x : p) :
@@ -201,10 +171,7 @@ theorem prodEquivOfIsCompl_symm_apply_left (h : IsCompl p q) (x : p) :
 #align submodule.prod_equiv_of_is_compl_symm_apply_left Submodule.prodEquivOfIsCompl_symm_apply_left
 
 /- warning: submodule.prod_equiv_of_is_compl_symm_apply_right -> Submodule.prodEquivOfIsCompl_symm_apply_right is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_right Submodule.prodEquivOfIsCompl_symm_apply_rightₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_right (h : IsCompl p q) (x : q) :
@@ -213,10 +180,7 @@ theorem prodEquivOfIsCompl_symm_apply_right (h : IsCompl p q) (x : q) :
 #align submodule.prod_equiv_of_is_compl_symm_apply_right Submodule.prodEquivOfIsCompl_symm_apply_right
 
 /- warning: submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero -> Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zeroₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
@@ -228,10 +192,7 @@ theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
 #align submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero
 
 /- warning: submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero -> Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zeroₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_snd_eq_zero (h : IsCompl p q) {x : E} :
@@ -243,10 +204,7 @@ theorem prodEquivOfIsCompl_symm_apply_snd_eq_zero (h : IsCompl p q) {x : E} :
 #align submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.prod_comm_trans_prod_equiv_of_is_compl Submodule.prodComm_trans_prodEquivOfIsComplₓ'. -/
 @[simp]
 theorem prodComm_trans_prodEquivOfIsCompl (h : IsCompl p q) :
@@ -268,10 +226,7 @@ def linearProjOfIsCompl (h : IsCompl p q) : E →ₗ[R] p :=
 variable {p q}
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_left Submodule.linearProjOfIsCompl_apply_leftₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_left (h : IsCompl p q) (x : p) :
@@ -279,10 +234,7 @@ theorem linearProjOfIsCompl_apply_left (h : IsCompl p q) (x : p) :
 #align submodule.linear_proj_of_is_compl_apply_left Submodule.linearProjOfIsCompl_apply_left
 
 /- warning: submodule.linear_proj_of_is_compl_range -> Submodule.linearProjOfIsCompl_range is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_range Submodule.linearProjOfIsCompl_rangeₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_range (h : IsCompl p q) : (linearProjOfIsCompl p q h).range = ⊤ :=
@@ -290,10 +242,7 @@ theorem linearProjOfIsCompl_range (h : IsCompl p q) : (linearProjOfIsCompl p q h
 #align submodule.linear_proj_of_is_compl_range Submodule.linearProjOfIsCompl_range
 
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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_eq_zero_iff Submodule.linearProjOfIsCompl_apply_eq_zero_iffₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
@@ -301,10 +250,7 @@ theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
 #align submodule.linear_proj_of_is_compl_apply_eq_zero_iff Submodule.linearProjOfIsCompl_apply_eq_zero_iff
 
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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right' Submodule.linearProjOfIsCompl_apply_right'ₓ'. -/
 theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q) :
     linearProjOfIsCompl p q h x = 0 :=
@@ -312,10 +258,7 @@ theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q
 #align submodule.linear_proj_of_is_compl_apply_right' Submodule.linearProjOfIsCompl_apply_right'
 
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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right Submodule.linearProjOfIsCompl_apply_rightₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_right (h : IsCompl p q) (x : q) :
@@ -324,10 +267,7 @@ theorem linearProjOfIsCompl_apply_right (h : IsCompl p q) (x : q) :
 #align submodule.linear_proj_of_is_compl_apply_right Submodule.linearProjOfIsCompl_apply_right
 
 /- warning: submodule.linear_proj_of_is_compl_ker -> Submodule.linearProjOfIsCompl_ker is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_ker Submodule.linearProjOfIsCompl_kerₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_ker (h : IsCompl p q) : (linearProjOfIsCompl p q h).ker = q :=
@@ -335,10 +275,7 @@ theorem linearProjOfIsCompl_ker (h : IsCompl p q) : (linearProjOfIsCompl p q h).
 #align submodule.linear_proj_of_is_compl_ker Submodule.linearProjOfIsCompl_ker
 
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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_comp_subtype Submodule.linearProjOfIsCompl_comp_subtypeₓ'. -/
 theorem linearProjOfIsCompl_comp_subtype (h : IsCompl p q) :
     (linearProjOfIsCompl p q h).comp p.Subtype = id :=
@@ -346,10 +283,7 @@ theorem linearProjOfIsCompl_comp_subtype (h : IsCompl p q) :
 #align submodule.linear_proj_of_is_compl_comp_subtype Submodule.linearProjOfIsCompl_comp_subtype
 
 /- warning: submodule.linear_proj_of_is_compl_idempotent -> Submodule.linearProjOfIsCompl_idempotent is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_idempotent Submodule.linearProjOfIsCompl_idempotentₓ'. -/
 theorem linearProjOfIsCompl_idempotent (h : IsCompl p q) (x : E) :
     linearProjOfIsCompl p q h (linearProjOfIsCompl p q h x) = linearProjOfIsCompl p q h x :=
@@ -357,10 +291,7 @@ theorem linearProjOfIsCompl_idempotent (h : IsCompl p q) (x : E) :
 #align submodule.linear_proj_of_is_compl_idempotent Submodule.linearProjOfIsCompl_idempotent
 
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 Case conversion may be inaccurate. Consider using '#align submodule.exists_unique_add_of_is_compl_prod Submodule.existsUnique_add_of_isCompl_prodₓ'. -/
 theorem existsUnique_add_of_isCompl_prod (hc : IsCompl p q) (x : E) :
     ∃! u : p × q, (u.fst : E) + u.snd = x :=
@@ -368,10 +299,7 @@ theorem existsUnique_add_of_isCompl_prod (hc : IsCompl p q) (x : E) :
 #align submodule.exists_unique_add_of_is_compl_prod Submodule.existsUnique_add_of_isCompl_prod
 
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 Case conversion may be inaccurate. Consider using '#align submodule.exists_unique_add_of_is_compl Submodule.existsUnique_add_of_isComplₓ'. -/
 theorem existsUnique_add_of_isCompl (hc : IsCompl p q) (x : E) :
     ∃ (u : p)(v : q), (u : E) + v = x ∧ ∀ (r : p) (s : q), (r : E) + s = x → r = u ∧ s = v :=
@@ -380,10 +308,7 @@ theorem existsUnique_add_of_isCompl (hc : IsCompl p q) (x : E) :
 #align submodule.exists_unique_add_of_is_compl Submodule.existsUnique_add_of_isCompl
 
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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q hpq)) x))) x
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_add_linear_proj_of_is_compl_eq_self Submodule.linear_proj_add_linearProjOfIsCompl_eq_selfₓ'. -/
 theorem linear_proj_add_linearProjOfIsCompl_eq_self (hpq : IsCompl p q) (x : E) :
     (p.linearProjOfIsCompl q hpq x + q.linearProjOfIsCompl p hpq.symm x : E) = x :=
@@ -400,10 +325,7 @@ namespace LinearMap
 open Submodule
 
 /- warning: linear_map.of_is_compl -> LinearMap.ofIsCompl is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl LinearMap.ofIsComplₓ'. -/
 /-- Given linear maps `φ` and `ψ` from complement submodules, `of_is_compl` is
 the induced linear map over the entire module. -/
@@ -414,10 +336,7 @@ def ofIsCompl {p q : Submodule R E} (h : IsCompl p q) (φ : p →ₗ[R] F) (ψ :
 variable {p q}
 
 /- warning: linear_map.of_is_compl_left_apply -> LinearMap.ofIsCompl_left_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_left_apply LinearMap.ofIsCompl_left_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (u : p) :
@@ -425,10 +344,7 @@ theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →
 #align linear_map.of_is_compl_left_apply LinearMap.ofIsCompl_left_apply
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_right_apply LinearMap.ofIsCompl_right_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (v : q) :
@@ -436,10 +352,7 @@ theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →
 #align linear_map.of_is_compl_right_apply LinearMap.ofIsCompl_right_apply
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_eq LinearMap.ofIsCompl_eqₓ'. -/
 theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : ∀ u, φ u = χ u) (hψ : ∀ u, ψ u = χ u) : ofIsCompl h φ ψ = χ :=
@@ -450,10 +363,7 @@ theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F}
 #align linear_map.of_is_compl_eq LinearMap.ofIsCompl_eq
 
 /- warning: linear_map.of_is_compl_eq' -> LinearMap.ofIsCompl_eq' is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_eq' LinearMap.ofIsCompl_eq'ₓ'. -/
 theorem ofIsCompl_eq' (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : φ = χ.comp p.Subtype) (hψ : ψ = χ.comp q.Subtype) : ofIsCompl h φ ψ = χ :=
@@ -461,10 +371,7 @@ theorem ofIsCompl_eq' (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F
 #align linear_map.of_is_compl_eq' LinearMap.ofIsCompl_eq'
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_zero LinearMap.ofIsCompl_zeroₓ'. -/
 @[simp]
 theorem ofIsCompl_zero (h : IsCompl p q) : (ofIsCompl h 0 0 : E →ₗ[R] F) = 0 :=
@@ -472,10 +379,7 @@ theorem ofIsCompl_zero (h : IsCompl p q) : (ofIsCompl h 0 0 : E →ₗ[R] F) = 0
 #align linear_map.of_is_compl_zero LinearMap.ofIsCompl_zero
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_add LinearMap.ofIsCompl_addₓ'. -/
 @[simp]
 theorem ofIsCompl_add (h : IsCompl p q) {φ₁ φ₂ : p →ₗ[R] F} {ψ₁ ψ₂ : q →ₗ[R] F} :
@@ -484,10 +388,7 @@ theorem ofIsCompl_add (h : IsCompl p q) {φ₁ φ₂ : p →ₗ[R] F} {ψ₁ ψ
 #align linear_map.of_is_compl_add LinearMap.ofIsCompl_add
 
 /- warning: linear_map.of_is_compl_smul -> LinearMap.ofIsCompl_smul is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {R : Type.{u3}} [_inst_11 : CommRing.{u3} R] {E : Type.{u2}} [_inst_12 : AddCommGroup.{u2} E] [_inst_13 : Module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12)] {F : Type.{u1}} [_inst_14 : AddCommGroup.{u1} F] [_inst_15 : Module.{u3, u1} R F (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14)] {p : Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} {q : Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} (h : IsCompl.{u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) 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(CommRing.toCommSemiring.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F 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(AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (instHSMul.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R E F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) 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(AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c (LinearMap.ofIsCompl.{u3, u2, u1} R (CommRing.toRing.{u3} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h φ ψ))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_smul LinearMap.ofIsCompl_smulₓ'. -/
 @[simp]
 theorem ofIsCompl_smul {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E]
@@ -501,10 +402,7 @@ section
 variable {R₁ : Type _} [CommRing R₁] [Module R₁ E] [Module R₁ F]
 
 /- warning: linear_map.of_is_compl_prod -> LinearMap.ofIsComplProd is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod LinearMap.ofIsComplProdₓ'. -/
 /-- The linear map from `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` to `E →ₗ[R₁] F`. -/
 def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
@@ -520,10 +418,7 @@ def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
 #align linear_map.of_is_compl_prod LinearMap.ofIsComplProd
 
 /- warning: linear_map.of_is_compl_prod_apply -> LinearMap.ofIsComplProd_apply is a dubious translation:
-lean 3 declaration is
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_inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) 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(CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) 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(CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_applyₓ'. -/
 @[simp]
 theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
@@ -532,10 +427,7 @@ theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
 #align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_apply
 
 /- warning: linear_map.of_is_compl_prod_equiv -> LinearMap.ofIsComplProdEquiv is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_equiv LinearMap.ofIsComplProdEquivₓ'. -/
 /-- The natural linear equivalence between `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` and `E →ₗ[R₁] F`. -/
 def ofIsComplProdEquiv {p q : Submodule R₁ E} (h : IsCompl p q) :
@@ -555,10 +447,7 @@ def ofIsComplProdEquiv {p q : Submodule R₁ E} (h : IsCompl p q) :
 end
 
 /- warning: linear_map.linear_proj_of_is_compl_of_proj -> LinearMap.linearProjOfIsCompl_of_proj is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.linear_proj_of_is_compl_of_proj LinearMap.linearProjOfIsCompl_of_projₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x) :
@@ -571,10 +460,7 @@ theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x
 #align linear_map.linear_proj_of_is_compl_of_proj LinearMap.linearProjOfIsCompl_of_proj
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.equiv_prod_of_surjective_of_is_compl LinearMap.equivProdOfSurjectiveOfIsComplₓ'. -/
 /-- If `f : E →ₗ[R] F` and `g : E →ₗ[R] G` are two surjective linear maps and
 their kernels are complement of each other, then `x ↦ (f x, g x)` defines
@@ -589,10 +475,7 @@ def equivProdOfSurjectiveOfIsCompl (f : E →ₗ[R] F) (g : E →ₗ[R] G) (hf :
 #align linear_map.equiv_prod_of_surjective_of_is_compl LinearMap.equivProdOfSurjectiveOfIsCompl
 
 /- warning: linear_map.coe_equiv_prod_of_surjective_of_is_compl -> LinearMap.coe_equivProdOfSurjectiveOfIsCompl is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_map.coe_equiv_prod_of_surjective_of_is_compl LinearMap.coe_equivProdOfSurjectiveOfIsComplₓ'. -/
 @[simp]
 theorem coe_equivProdOfSurjectiveOfIsCompl {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
@@ -602,10 +485,7 @@ theorem coe_equivProdOfSurjectiveOfIsCompl {f : E →ₗ[R] F} {g : E →ₗ[R]
 #align linear_map.coe_equiv_prod_of_surjective_of_is_compl LinearMap.coe_equivProdOfSurjectiveOfIsCompl
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.equiv_prod_of_surjective_of_is_compl_apply LinearMap.equivProdOfSurjectiveOfIsCompl_applyₓ'. -/
 @[simp]
 theorem equivProdOfSurjectiveOfIsCompl_apply {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
@@ -621,10 +501,7 @@ namespace Submodule
 open LinearMap
 
 /- warning: submodule.is_compl_equiv_proj -> Submodule.isComplEquivProj is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align submodule.is_compl_equiv_proj Submodule.isComplEquivProjₓ'. -/
 /-- Equivalence between submodules `q` such that `is_compl p q` and linear maps `f : E →ₗ[R] p`
 such that `∀ x : p, f x = x`. -/
@@ -637,10 +514,7 @@ def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p
 #align submodule.is_compl_equiv_proj Submodule.isComplEquivProj
 
 /- warning: submodule.coe_is_compl_equiv_proj_apply -> Submodule.coe_isComplEquivProj_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
@@ -649,10 +523,7 @@ theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
 #align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_apply
 
 /- warning: submodule.coe_is_compl_equiv_proj_symm_apply -> Submodule.coe_isComplEquivProj_symm_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_symm_apply Submodule.coe_isComplEquivProj_symm_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_symm_apply (f : { f : E →ₗ[R] p // ∀ x : p, f x = x }) :
@@ -680,10 +551,7 @@ structure IsProj {F : Type _} [FunLike F M fun _ => M] (f : F) : Prop where
 -/
 
 /- warning: linear_map.is_proj_iff_idempotent -> LinearMap.isProj_iff_idempotent is a dubious translation:
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj_iff_idempotent LinearMap.isProj_iff_idempotentₓ'. -/
 theorem isProj_iff_idempotent (f : M →ₗ[S] M) : (∃ p : Submodule S M, IsProj p f) ↔ f ∘ₗ f = f :=
   by
@@ -708,10 +576,7 @@ namespace IsProj
 variable {p m}
 
 /- warning: linear_map.is_proj.cod_restrict -> LinearMap.IsProj.codRestrict is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict LinearMap.IsProj.codRestrictₓ'. -/
 /-- Restriction of the codomain of a projection of onto a subspace `p` to `p` instead of the whole
 space.
@@ -721,10 +586,7 @@ def codRestrict {f : M →ₗ[S] M} (h : IsProj m f) : M →ₗ[S] m :=
 #align linear_map.is_proj.cod_restrict LinearMap.IsProj.codRestrict
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply LinearMap.IsProj.codRestrict_applyₓ'. -/
 @[simp]
 theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.codRestrict x) = f x :=
@@ -732,10 +594,7 @@ theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.c
 #align linear_map.is_proj.cod_restrict_apply LinearMap.IsProj.codRestrict_apply
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_codₓ'. -/
 @[simp]
 theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.codRestrict x = x :=
@@ -746,20 +605,14 @@ theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.c
 #align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_cod
 
 /- warning: linear_map.is_proj.cod_restrict_ker -> LinearMap.IsProj.codRestrict_ker is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_ker LinearMap.IsProj.codRestrict_kerₓ'. -/
 theorem codRestrict_ker {f : M →ₗ[S] M} (h : IsProj m f) : h.codRestrict.ker = f.ker :=
   f.ker_codRestrict m _
 #align linear_map.is_proj.cod_restrict_ker LinearMap.IsProj.codRestrict_ker
 
 /- warning: linear_map.is_proj.is_compl -> LinearMap.IsProj.isCompl is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.is_compl LinearMap.IsProj.isComplₓ'. -/
 theorem isCompl {f : E →ₗ[R] E} (h : IsProj p f) : IsCompl p f.ker :=
   by
@@ -768,10 +621,7 @@ theorem isCompl {f : E →ₗ[R] E} (h : IsProj p f) : IsCompl p f.ker :=
 #align linear_map.is_proj.is_compl LinearMap.IsProj.isCompl
 
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_inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.IsProj.isCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f h))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map' LinearMap.IsProj.eq_conj_prod_map'ₓ'. -/
 theorem eq_conj_prod_map' {f : E →ₗ[R] E} (h : IsProj p f) :
     f =
@@ -805,10 +655,7 @@ namespace LinearMap
 variable {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E] {p : Submodule R E}
 
 /- warning: linear_map.is_proj.eq_conj_prod_map -> LinearMap.IsProj.eq_conj_prodMap is a dubious translation:
-lean 3 declaration is
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Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map LinearMap.IsProj.eq_conj_prodMapₓ'. -/
 theorem IsProj.eq_conj_prodMap {f : E →ₗ[R] E} (h : IsProj p f) :
     f = (p.prodEquivOfIsCompl f.ker h.IsCompl).conj (prodMap id 0) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -51,7 +51,7 @@ open Submodule
 lean 3 declaration is
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(Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (instHSub.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.hasSub.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (LinearMap.id.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} R R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.subtype.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) f))) p)
 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)}, (forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) x) -> (Eq.{succ u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (instHSub.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSubLinearMapToAddCommMonoid.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (LinearMap.id.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (LinearMap.comp.{u2, u2, u2, u1, u1, u1} R R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.subtype.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) f))) p)
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)}, (forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) x) -> (Eq.{succ u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (LinearMap.id.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (LinearMap.comp.{u2, u2, u2, u1, u1, u1} R R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align linear_map.ker_id_sub_eq_of_proj LinearMap.ker_id_sub_eq_of_projₓ'. -/
 theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
     ker (id - p.Subtype.comp f) = p := by
@@ -64,7 +64,7 @@ theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
 lean 3 declaration is
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 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (Submodule.instTopSubmodule.{u2, u1} R (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p))))
 Case conversion may be inaccurate. Consider using '#align linear_map.range_eq_of_proj LinearMap.range_eq_of_projₓ'. -/
 theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f = ⊤ :=
   range_eq_top.2 fun x => ⟨x, hf x⟩
@@ -74,7 +74,7 @@ theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f
 lean 3 declaration is
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 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)}, (forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E 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+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)}, (forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E 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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) x) -> (IsCompl.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
 Case conversion may be inaccurate. Consider using '#align linear_map.is_compl_of_proj LinearMap.isCompl_of_projₓ'. -/
 theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl p f.ker :=
   by
@@ -114,7 +114,7 @@ def quotientEquivOfIsCompl (h : IsCompl p q) : (E ⧸ p) ≃ₗ[R] q :=
 lean 3 declaration is
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_inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) E (coeSubtype.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q))))) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) => HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Subtype.{succ 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_inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (fun (_x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) => HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (SMulZeroClass.toSMul.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q))) (DistribSMul.toSMulZeroClass.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q))) (DistribMulAction.toDistribSMul.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E 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(Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.quotientEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) x) (Submodule.Quotient.mk.{u1, u2} R E _inst_1 _inst_2 _inst_3 p (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl_symm_apply Submodule.quotientEquivOfIsCompl_symm_applyₓ'. -/
 @[simp]
 theorem quotientEquivOfIsCompl_symm_apply (h : IsCompl p q) (x : q) :
@@ -126,7 +126,7 @@ theorem quotientEquivOfIsCompl_symm_apply (h : IsCompl p q) (x : q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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 but is expected to have type
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u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} 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_inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E 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(Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} 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u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Submodule.quotientEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Submodule.Quotient.mk.{u1, u2} R E _inst_1 _inst_2 _inst_3 p (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x))) x
 Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl_apply_mk_coe Submodule.quotientEquivOfIsCompl_apply_mk_coeₓ'. -/
 @[simp]
 theorem quotientEquivOfIsCompl_apply_mk_coe (h : IsCompl p q) (x : q) :
@@ -138,7 +138,7 @@ theorem quotientEquivOfIsCompl_apply_mk_coe (h : IsCompl p q) (x : q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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 but is expected to have type
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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Submodule.quotientEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x))) x
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R E _inst_1 _inst_2 _inst_3 p (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E 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u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} 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 Case conversion may be inaccurate. Consider using '#align submodule.mk_quotient_equiv_of_is_compl_apply Submodule.mk_quotientEquivOfIsCompl_applyₓ'. -/
 @[simp]
 theorem mk_quotientEquivOfIsCompl_apply (h : IsCompl p q) (x : E ⧸ p) :
@@ -180,7 +180,7 @@ theorem coe_prodEquivOfIsCompl (h : IsCompl p q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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 Case conversion may be inaccurate. Consider using '#align submodule.coe_prod_equiv_of_is_compl' Submodule.coe_prodEquivOfIsCompl'ₓ'. -/
 @[simp]
 theorem coe_prodEquivOfIsCompl' (h : IsCompl p q) (x : p × q) :
@@ -192,7 +192,7 @@ theorem coe_prodEquivOfIsCompl' (h : IsCompl p q) (x : p × q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_left Submodule.prodEquivOfIsCompl_symm_apply_leftₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_left (h : IsCompl p q) (x : p) :
@@ -204,7 +204,7 @@ theorem prodEquivOfIsCompl_symm_apply_left (h : IsCompl p q) (x : p) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_right Submodule.prodEquivOfIsCompl_symm_apply_rightₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_right (h : IsCompl p q) (x : q) :
@@ -216,7 +216,7 @@ theorem prodEquivOfIsCompl_symm_apply_right (h : IsCompl p q) (x : q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)
 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zeroₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
@@ -231,7 +231,7 @@ theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)
 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zeroₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_snd_eq_zero (h : IsCompl p q) {x : E} :
@@ -271,7 +271,7 @@ variable {p q}
 lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (coeSubtype.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p))))) x)) x
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_left Submodule.linearProjOfIsCompl_apply_leftₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_left (h : IsCompl p q) (x : p) :
@@ -293,7 +293,7 @@ theorem linearProjOfIsCompl_range (h : IsCompl p q) : (linearProjOfIsCompl p q h
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) {x : E}, Iff (Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => E -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 0 (OfNat.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 0 (Zero.zero.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))))) (Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) {x : E}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))) (Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) {x : E}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))) (Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_eq_zero_iff Submodule.linearProjOfIsCompl_apply_eq_zero_iffₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
@@ -304,7 +304,7 @@ theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : E), (Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q) -> (Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 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(Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => E -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 0 (OfNat.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 0 (Zero.zero.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right' Submodule.linearProjOfIsCompl_apply_right'ₓ'. -/
 theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q) :
     linearProjOfIsCompl p q h x = 0 :=
@@ -315,7 +315,7 @@ theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right Submodule.linearProjOfIsCompl_apply_rightₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_right (h : IsCompl p q) (x : q) :
@@ -349,7 +349,7 @@ theorem linearProjOfIsCompl_comp_subtype (h : IsCompl p q) :
 lean 3 declaration is
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_idempotent Submodule.linearProjOfIsCompl_idempotentₓ'. -/
 theorem linearProjOfIsCompl_idempotent (h : IsCompl p q) (x : E) :
     linearProjOfIsCompl p q h (linearProjOfIsCompl p q h x) = linearProjOfIsCompl p q h x :=
@@ -383,7 +383,7 @@ theorem existsUnique_add_of_isCompl (hc : IsCompl p q) (x : E) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (hpq : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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 but is expected to have type
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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 q p (IsCompl.symm.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q hpq)) x))) x
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (hpq : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : E), Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) (FunLike.coe.{succ u2, succ u2, succ u2} 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q hpq)) x))) x
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_add_linear_proj_of_is_compl_eq_self Submodule.linear_proj_add_linearProjOfIsCompl_eq_selfₓ'. -/
 theorem linear_proj_add_linearProjOfIsCompl_eq_self (hpq : IsCompl p q) (x : E) :
     (p.linearProjOfIsCompl q hpq x + q.linearProjOfIsCompl p hpq.symm x : E) = x :=
@@ -417,7 +417,7 @@ variable {p q}
 lean 3 declaration is
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 but is expected to have type
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(LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) φ u)
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_left_apply LinearMap.ofIsCompl_left_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (u : p) :
@@ -428,7 +428,7 @@ theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →
 lean 3 declaration is
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 but is expected to have type
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(LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) ψ v)
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_right_apply LinearMap.ofIsCompl_right_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (v : q) :
@@ -439,7 +439,7 @@ theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_eq LinearMap.ofIsCompl_eqₓ'. -/
 theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : ∀ u, φ u = χ u) (hψ : ∀ u, ψ u = χ u) : ofIsCompl h φ ψ = χ :=
@@ -523,7 +523,7 @@ def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} (h : IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.partialOrder.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ 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_inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u1, u2} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E 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(SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ 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 but is expected to have type
-  forall {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_13 : Module.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} {q : Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} (h : IsCompl.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) 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(CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ E F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u2, u1, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u2, u1} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ))
+  forall {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_13 : Module.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} {q : Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} (h : IsCompl.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) p q) (φ : Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ 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(CommRing.toCommSemiring.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) 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x q)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) 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(CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ 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_inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F 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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_applyₓ'. -/
 @[simp]
 theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
@@ -558,7 +558,7 @@ end
 lean 3 declaration is
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 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (hf : forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E 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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) x), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (Submodule.linearProjOfIsCompl.{u2, u1} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R 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(Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.isCompl_of_proj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f hf)) f
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (hf : forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} 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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (Submodule.linearProjOfIsCompl.{u2, u1} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E 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_inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.isCompl_of_proj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f hf)) f
 Case conversion may be inaccurate. Consider using '#align linear_map.linear_proj_of_is_compl_of_proj LinearMap.linearProjOfIsCompl_of_projₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x) :
@@ -605,7 +605,7 @@ theorem coe_equivProdOfSurjectiveOfIsCompl {f : E →ₗ[R] F} {g : E →ₗ[R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {G : Type.{u4}} [_inst_6 : AddCommGroup.{u4} G] [_inst_7 : Module.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6)] {f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5} {g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7} (hf : Eq.{succ u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) (Top.top.{u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (Submodule.hasTop.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5))) (hg : Eq.{succ u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g) (Top.top.{u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (Submodule.hasTop.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7))) (hfg : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) 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 but is expected to have type
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(DistribMulAction.toDistribSMul.{u4, max u2 u1} R (Prod.{u2, u1} F G) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Prod.{u2, u1} F G) (Prod.instAddCommMonoidSum.{u2, u1} F G (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6))) (Module.toDistribMulAction.{u4, max u2 u1} R (Prod.{u2, u1} F G) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} F G (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)) (Prod.module.{u4, u2, u1} R F G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_5 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u4, u3, max u2 u1} (LinearEquiv.{u4, u4, u3, max u1 u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R 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(AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)) _inst_3 (Prod.module.{u4, u2, u1} R F G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_5 _inst_7) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, u3, max u2 u1} R R E (Prod.{u2, u1} F G) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (Prod.instAddCommMonoidSum.{u2, u1} F G (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)) _inst_3 (Prod.module.{u4, u2, u1} R F G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_5 _inst_7) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1))))))) (LinearMap.equivProdOfSurjectiveOfIsCompl.{u4, u3, u2, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 G _inst_6 _inst_7 f g hf hg hfg) x) (Prod.mk.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => F) x) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => G) x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R E F (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) f x) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => G) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u1} R R E G (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g x))
+  forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u4, u3} R E (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] [_inst_5 : Module.{u4, u2} R F (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {G : Type.{u1}} [_inst_6 : AddCommGroup.{u1} G] [_inst_7 : Module.{u4, u1} R G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)] {f : LinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5} {g : LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7} (hf : Eq.{succ u2} (Submodule.{u4, u2} R F (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_5) (LinearMap.range.{u4, u4, u3, u2, max u3 u2} R R E F (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u4, u4, u3, u2} R R E F (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) f) (Top.top.{u2} (Submodule.{u4, u2} R F (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_5) (Submodule.instTopSubmodule.{u4, u2} R F (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_5))) (hg : Eq.{succ u1} (Submodule.{u4, u1} R G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_7) (LinearMap.range.{u4, u4, u3, u1, max u3 u1} R R E G (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u4, u4, u3, u1} R R E G (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) g) (Top.top.{u1} (Submodule.{u4, u1} R G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_7) (Submodule.instTopSubmodule.{u4, u1} R G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_7))) (hfg : IsCompl.{u3} (Submodule.{u4, u3} R E 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_inst_2))) (DistribMulAction.toDistribSMul.{u4, u3} R E (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)) (Module.toDistribMulAction.{u4, u3} R E (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u4, max u2 u1} R (Prod.{u2, u1} F G) (AddMonoid.toZero.{max u2 u1} (Prod.{u2, u1} F G) (AddCommMonoid.toAddMonoid.{max u2 u1} (Prod.{u2, u1} F G) (Prod.instAddCommMonoidSum.{u2, u1} F G (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)))) (DistribSMul.toSMulZeroClass.{u4, max u2 u1} R (Prod.{u2, u1} F G) (AddMonoid.toAddZeroClass.{max u2 u1} (Prod.{u2, u1} F G) (AddCommMonoid.toAddMonoid.{max u2 u1} (Prod.{u2, u1} F G) (Prod.instAddCommMonoidSum.{u2, u1} F G (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)))) (DistribMulAction.toDistribSMul.{u4, max u2 u1} R (Prod.{u2, u1} F G) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Prod.{u2, u1} F G) (Prod.instAddCommMonoidSum.{u2, u1} F G (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6))) (Module.toDistribMulAction.{u4, max u2 u1} R (Prod.{u2, u1} F G) (Ring.toSemiring.{u4} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u1} F G (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)) (Prod.module.{u4, u2, u1} R F G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_5 _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u4, u3, max u2 u1} (LinearEquiv.{u4, u4, u3, max u1 u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R 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(AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_5 _inst_7) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1))))))) (LinearMap.equivProdOfSurjectiveOfIsCompl.{u4, u3, u2, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 G _inst_6 _inst_7 f g hf hg hfg) x) (Prod.mk.{u2, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) x) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => G) x) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R E F (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) f x) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => G) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u1} R R E G (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g x))
 Case conversion may be inaccurate. Consider using '#align linear_map.equiv_prod_of_surjective_of_is_compl_apply LinearMap.equivProdOfSurjectiveOfIsCompl_applyₓ'. -/
 @[simp]
 theorem equivProdOfSurjectiveOfIsCompl_apply {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
@@ -624,7 +624,7 @@ open LinearMap
 lean 3 declaration is
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 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), Equiv.{succ u2, succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align submodule.is_compl_equiv_proj Submodule.isComplEquivProjₓ'. -/
 /-- Equivalence between submodules `q` such that `is_compl p q` and linear maps `f : E →ₗ[R] p`
 such that `∀ x : p, f x = x`. -/
@@ -640,7 +640,7 @@ def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p
 lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q)) (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (coeSubtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q))))) q) (Subtype.property.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R 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 but is expected to have type
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_inst_2) _inst_3) p)) x)) x))) (Submodule.isComplEquivProj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p) q)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p (Subtype.val.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) q) (Subtype.property.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) 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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q)), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x))) (Submodule.isComplEquivProj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p) q)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p (Subtype.val.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) q) (Subtype.property.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) q))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
@@ -652,7 +652,7 @@ theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
 lean 3 declaration is
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 but is expected to have type
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Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (a : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x) f))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_symm_apply Submodule.coe_isComplEquivProj_symm_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_symm_apply (f : { f : E →ₗ[R] p // ∀ x : p, f x = x }) :
@@ -724,7 +724,7 @@ def codRestrict {f : M →ₗ[S] M} (h : IsProj m f) : M →ₗ[S] m :=
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S M M (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)))))) f) (x : M), Eq.{succ u2} M ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) x m))))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) => M -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} S S M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) (LinearMap.IsProj.codRestrict.{u1, u2} S _inst_8 M _inst_9 _inst_10 m f h) x)) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) f x)
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) x) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f x)
+  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) x) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f x)
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply LinearMap.IsProj.codRestrict_applyₓ'. -/
 @[simp]
 theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.codRestrict x) = f x :=
@@ -735,7 +735,7 @@ theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.c
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S M M (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)))))) f) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) => M -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} S S M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) (LinearMap.IsProj.codRestrict.{u1, u2} S _inst_8 M _inst_9 _inst_10 m f h) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) x m))))) x)) x
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) x
+  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) x
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_codₓ'. -/
 @[simp]
 theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.codRestrict x = x :=
@@ -808,7 +808,7 @@ variable {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E] {p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u1, u2, u2} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R E E (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) f), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) f (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearEquiv.conj._proof_3.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearEquiv.conj._proof_4.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Module.End.{u1, u2} R (Prod.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R 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_inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u2, u1, u1} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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(LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f))) (LinearMap.instZeroLinearMap.{u2, u2, u1, u1} R R (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u2, u1, u1} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map LinearMap.IsProj.eq_conj_prodMapₓ'. -/
 theorem IsProj.eq_conj_prodMap {f : E →ₗ[R] E} (h : IsProj p f) :
     f = (p.prodEquivOfIsCompl f.ker h.IsCompl).conj (prodMap id 0) :=

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

@@ -640,7 +640,7 @@ def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p
 lean 3 declaration is
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 but is expected to have type
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_inst_2) _inst_3) p)) x)) x))) (Submodule.isComplEquivProj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p) q)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p (Subtype.val.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) q) (Subtype.property.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) 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_inst_2) _inst_3) p)) x)) x))) (Submodule.isComplEquivProj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p) q)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p (Subtype.val.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) 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_inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) q))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
@@ -652,7 +652,7 @@ theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_symm_apply Submodule.coe_isComplEquivProj_symm_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_symm_apply (f : { f : E →ₗ[R] p // ∀ x : p, f x = x }) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -51,7 +51,7 @@ open Submodule
 lean 3 declaration is
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 but is expected to have type
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(Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (instHSub.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSubLinearMapToAddCommMonoid.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (LinearMap.id.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (LinearMap.comp.{u2, u2, u2, u1, u1, u1} R R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.subtype.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) f))) p)
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)}, (forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) x) -> (Eq.{succ u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (LinearMap.id.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (LinearMap.comp.{u2, u2, u2, u1, u1, u1} R R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (Submodule.subtype.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) f))) p)
 Case conversion may be inaccurate. Consider using '#align linear_map.ker_id_sub_eq_of_proj LinearMap.ker_id_sub_eq_of_projₓ'. -/
 theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
     ker (id - p.Subtype.comp f) = p := by
@@ -64,7 +64,7 @@ theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align linear_map.range_eq_of_proj LinearMap.range_eq_of_projₓ'. -/
 theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f = ⊤ :=
   range_eq_top.2 fun x => ⟨x, hf x⟩
@@ -74,7 +74,7 @@ theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f
 lean 3 declaration is
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(Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)}, (forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)}, (forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E 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R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) x) -> (IsCompl.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E 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(Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
 Case conversion may be inaccurate. Consider using '#align linear_map.is_compl_of_proj LinearMap.isCompl_of_projₓ'. -/
 theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl p f.ker :=
   by
@@ -271,7 +271,7 @@ variable {p q}
 lean 3 declaration is
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(Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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(SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (coeSubtype.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p))))) x)) x
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_left Submodule.linearProjOfIsCompl_apply_leftₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_left (h : IsCompl p q) (x : p) :
@@ -282,7 +282,7 @@ theorem linearProjOfIsCompl_apply_left (h : IsCompl p q) (x : p) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (Submodule.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.range.{u1, u1, u2, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) (Top.top.{u2} (Submodule.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.range.{u1, u1, u2, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) (Top.top.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (Submodule.instTopSubmodule.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => 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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.range.{u1, u1, u2, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) (Top.top.{u2} (Submodule.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (Submodule.instTopSubmodule.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_range Submodule.linearProjOfIsCompl_rangeₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_range (h : IsCompl p q) : (linearProjOfIsCompl p q h).range = ⊤ :=
@@ -293,7 +293,7 @@ theorem linearProjOfIsCompl_range (h : IsCompl p q) : (linearProjOfIsCompl p q h
 lean 3 declaration is
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(Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) {x : E}, Iff (Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} 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(Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 0 (OfNat.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 0 (Zero.zero.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))))) (Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)
 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))) (Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) {x : E}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))) (Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_eq_zero_iff Submodule.linearProjOfIsCompl_apply_eq_zero_iffₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
@@ -304,7 +304,7 @@ theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
 lean 3 declaration is
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(Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : E), (Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q) -> (Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 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u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 0 (Zero.zero.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : E), (Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : E), (Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))))
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right' Submodule.linearProjOfIsCompl_apply_right'ₓ'. -/
 theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q) :
     linearProjOfIsCompl p q h x = 0 :=
@@ -315,7 +315,7 @@ theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E 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u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right Submodule.linearProjOfIsCompl_apply_rightₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_right (h : IsCompl p q) (x : q) :
@@ -327,7 +327,7 @@ theorem linearProjOfIsCompl_apply_right (h : IsCompl p q) (x : q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) q
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) q
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) q
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_ker Submodule.linearProjOfIsCompl_kerₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_ker (h : IsCompl p q) : (linearProjOfIsCompl p q h).ker = q :=
@@ -349,7 +349,7 @@ theorem linearProjOfIsCompl_comp_subtype (h : IsCompl p q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_idempotent Submodule.linearProjOfIsCompl_idempotentₓ'. -/
 theorem linearProjOfIsCompl_idempotent (h : IsCompl p q) (x : E) :
     linearProjOfIsCompl p q h (linearProjOfIsCompl p q h x) = linearProjOfIsCompl p q h x :=
@@ -383,7 +383,7 @@ theorem existsUnique_add_of_isCompl (hc : IsCompl p q) (x : E) :
 lean 3 declaration is
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 but is expected to have type
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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q hpq)) x))) x
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (hpq : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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_inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q hpq) x)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 q p (IsCompl.symm.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q hpq)) x))) x
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_add_linear_proj_of_is_compl_eq_self Submodule.linear_proj_add_linearProjOfIsCompl_eq_selfₓ'. -/
 theorem linear_proj_add_linearProjOfIsCompl_eq_self (hpq : IsCompl p q) (x : E) :
     (p.linearProjOfIsCompl q hpq x + q.linearProjOfIsCompl p hpq.symm x : E) = x :=
@@ -417,7 +417,7 @@ variable {p q}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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(_x : Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) => F) _x) 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+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) p q) {φ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5} {ψ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5} (u : Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => F) (Subtype.val.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Set.{u3} E) 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(LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) φ u)
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_left_apply LinearMap.ofIsCompl_left_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (u : p) :
@@ -428,7 +428,7 @@ theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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(_x : Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) => F) _x) 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+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) p q) {φ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5} {ψ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5} (v : Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => F) (Subtype.val.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Set.{u3} E) 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(LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) ψ v)
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_right_apply LinearMap.ofIsCompl_right_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (v : q) :
@@ -439,7 +439,7 @@ theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_eq LinearMap.ofIsCompl_eqₓ'. -/
 theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : ∀ u, φ u = χ u) (hψ : ∀ u, ψ u = χ u) : ofIsCompl h φ ψ = χ :=
@@ -523,7 +523,7 @@ def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} (h : IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.partialOrder.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ 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_inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F 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(Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_2.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_3.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u1, u2, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u1, u2} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) φ))
 but is expected to have type
-  forall {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_13 : Module.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} {q : Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} (h : IsCompl.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) p q) (φ : Prod.{max u1 u2, max u1 u2} 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x q)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) 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_inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ E F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ 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(Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E 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(CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ 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(CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u2, u1, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u2, u1} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ))
+  forall {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_13 : Module.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} {q : Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} (h : IsCompl.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) p q) (φ : Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ 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(CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ E F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u2, u1, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u2, u1} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ))
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_applyₓ'. -/
 @[simp]
 theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
@@ -558,7 +558,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (hf : forall (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E 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 but is expected to have type
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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (Submodule.linearProjOfIsCompl.{u2, u1} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R 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_inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.isCompl_of_proj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f hf)) f
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (hf : forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) x), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (Submodule.linearProjOfIsCompl.{u2, u1} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E 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_inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.isCompl_of_proj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f hf)) f
 Case conversion may be inaccurate. Consider using '#align linear_map.linear_proj_of_is_compl_of_proj LinearMap.linearProjOfIsCompl_of_projₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x) :
@@ -574,7 +574,7 @@ theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {G : Type.{u4}} [_inst_6 : AddCommGroup.{u4} G] [_inst_7 : Module.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7), (Eq.{succ u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.equivProdOfSurjectiveOfIsCompl._proof_1.{u1} R _inst_1) f) (Top.top.{u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (Submodule.hasTop.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5))) -> (Eq.{succ u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.equivProdOfSurjectiveOfIsCompl._proof_2.{u1} R _inst_1) g) (Top.top.{u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (Submodule.hasTop.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7))) -> (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) g)) -> (LinearEquiv.{u1, u1, u2, max u3 u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.equivProdOfSurjectiveOfIsCompl._proof_3.{u1} R _inst_1) (LinearMap.equivProdOfSurjectiveOfIsCompl._proof_4.{u1} R _inst_1) E (Prod.{u3, u4} F G) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Prod.addCommMonoid.{u3, u4} F G (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6)) _inst_3 (Prod.module.{u1, u3, u4} R F G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_5 _inst_7))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {G : Type.{u4}} [_inst_6 : AddCommGroup.{u4} G] [_inst_7 : Module.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7), (Eq.{succ u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) (Top.top.{u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (Submodule.instTopSubmodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5))) -> (Eq.{succ u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g) (Top.top.{u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (Submodule.instTopSubmodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7))) -> (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) g)) -> (LinearEquiv.{u1, u1, u2, max u4 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) E (Prod.{u3, u4} F G) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Prod.instAddCommMonoidSum.{u3, u4} F G (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6)) _inst_3 (Prod.module.{u1, u3, u4} R F G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_5 _inst_7))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {G : Type.{u4}} [_inst_6 : AddCommGroup.{u4} G] [_inst_7 : Module.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7), (Eq.{succ u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) (Top.top.{u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (Submodule.instTopSubmodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5))) -> (Eq.{succ u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g) (Top.top.{u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (Submodule.instTopSubmodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7))) -> (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) g)) -> (LinearEquiv.{u1, u1, u2, max u4 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) E (Prod.{u3, u4} F G) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Prod.instAddCommMonoidSum.{u3, u4} F G (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6)) _inst_3 (Prod.module.{u1, u3, u4} R F G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_5 _inst_7))
 Case conversion may be inaccurate. Consider using '#align linear_map.equiv_prod_of_surjective_of_is_compl LinearMap.equivProdOfSurjectiveOfIsComplₓ'. -/
 /-- If `f : E →ₗ[R] F` and `g : E →ₗ[R] G` are two surjective linear maps and
 their kernels are complement of each other, then `x ↦ (f x, g x)` defines
@@ -592,7 +592,7 @@ def equivProdOfSurjectiveOfIsCompl (f : E →ₗ[R] F) (g : E →ₗ[R] G) (hf :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {G : Type.{u4}} [_inst_6 : AddCommGroup.{u4} G] [_inst_7 : Module.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6)] {f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5} {g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7} (hf : Eq.{succ u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) (Top.top.{u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (Submodule.hasTop.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5))) (hg : Eq.{succ u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g) (Top.top.{u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (Submodule.hasTop.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7))) (hfg : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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 but is expected to have type
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_inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u3, u1} R R E G (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g)), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u4, u4, u3, max u2 u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E 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_inst_6)) _inst_3 (Prod.module.{u4, u2, u1} R F G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_5 _inst_7) (LinearMap.equivProdOfSurjectiveOfIsCompl.{u4, u3, u2, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 G _inst_6 _inst_7 f g hf hg hfg)) (LinearMap.prod.{u4, u3, u2, u1} R E F G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_5 _inst_7 f g)
+  forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u4, u3} R E (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] [_inst_5 : Module.{u4, u2} R F (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {G : Type.{u1}} [_inst_6 : AddCommGroup.{u1} G] [_inst_7 : Module.{u4, u1} R G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)] {f : LinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5} {g : LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7} (hf : Eq.{succ u2} (Submodule.{u4, u2} R F (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_5) (LinearMap.range.{u4, u4, u3, u2, max u3 u2} R R E F (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u4, u4, u3, u2} R R E F (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) f) (Top.top.{u2} (Submodule.{u4, u2} R F (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_5) (Submodule.instTopSubmodule.{u4, u2} R F (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_5))) (hg : Eq.{succ u1} (Submodule.{u4, u1} R G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_7) (LinearMap.range.{u4, u4, u3, u1, max u3 u1} R R E G (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u4, u4, u3, u1} R R E G (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (RingHomSurjective.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) g) (Top.top.{u1} (Submodule.{u4, u1} R G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_7) (Submodule.instTopSubmodule.{u4, u1} R G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_7))) (hfg : IsCompl.{u3} (Submodule.{u4, u3} R E (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u4, u3} R E (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u4, u3} R E (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u4, u3} R E (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u3} (Submodule.{u4, u3} R E (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u4, u3} R E (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) (LinearMap.ker.{u4, u4, u3, u2, max u3 u2} R R E F (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u4, u4, u3, u2} R R E F (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) f) (LinearMap.ker.{u4, u4, u3, u1, max u3 u1} R R E G (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u4, u4, u3, u1} R R E G (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g)), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (LinearMap.{u4, u4, u3, max u2 u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E (Prod.{u2, u1} F G) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (Prod.instAddCommMonoidSum.{u2, u1} F G (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)) _inst_3 (Prod.module.{u4, u2, u1} R F G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_5 _inst_7)) (LinearEquiv.toLinearMap.{u4, u4, u3, max u2 u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R _inst_1)) E (Prod.{u2, u1} F G) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (Prod.instAddCommMonoidSum.{u2, u1} F G (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)) _inst_3 (Prod.module.{u4, u2, u1} R F G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_5 _inst_7) (LinearMap.equivProdOfSurjectiveOfIsCompl.{u4, u3, u2, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 G _inst_6 _inst_7 f g hf hg hfg)) (LinearMap.prod.{u4, u3, u2, u1} R E F G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_5 _inst_7 f g)
 Case conversion may be inaccurate. Consider using '#align linear_map.coe_equiv_prod_of_surjective_of_is_compl LinearMap.coe_equivProdOfSurjectiveOfIsComplₓ'. -/
 @[simp]
 theorem coe_equivProdOfSurjectiveOfIsCompl {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
@@ -605,7 +605,7 @@ theorem coe_equivProdOfSurjectiveOfIsCompl {f : E →ₗ[R] F} {g : E →ₗ[R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {G : Type.{u4}} [_inst_6 : AddCommGroup.{u4} G] [_inst_7 : Module.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6)] {f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5} {g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7} (hf : Eq.{succ u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) (Top.top.{u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (Submodule.hasTop.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5))) (hg : Eq.{succ u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g) (Top.top.{u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (Submodule.hasTop.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7))) (hfg : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) 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 but is expected to have type
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+  forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u4, u3} R E (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] [_inst_5 : Module.{u4, u2} R F (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {G : Type.{u1}} [_inst_6 : AddCommGroup.{u1} G] [_inst_7 : Module.{u4, u1} R G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)] {f : LinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5} {g : LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R 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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R E F (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) f x) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => G) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u1} R R E G (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g x))
 Case conversion may be inaccurate. Consider using '#align linear_map.equiv_prod_of_surjective_of_is_compl_apply LinearMap.equivProdOfSurjectiveOfIsCompl_applyₓ'. -/
 @[simp]
 theorem equivProdOfSurjectiveOfIsCompl_apply {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
@@ -624,7 +624,7 @@ open LinearMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), Equiv.{succ u2, succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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_inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => forall (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => E -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (coeSubtype.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p))))) x)) x))
 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), Equiv.{succ u2, succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align submodule.is_compl_equiv_proj Submodule.isComplEquivProjₓ'. -/
 /-- Equivalence between submodules `q` such that `is_compl p q` and linear maps `f : E →ₗ[R] p`
 such that `∀ x : p, f x = x`. -/
@@ -640,7 +640,7 @@ def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p
 lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q)) (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (coeSubtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q))))) q) (Subtype.property.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R 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 but is expected to have type
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_inst_2) _inst_3) p)) x)) x))) (Submodule.isComplEquivProj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p) q)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p (Subtype.val.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) q) (Subtype.property.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) 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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q)), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x))) (Submodule.isComplEquivProj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p) q)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p (Subtype.val.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) q) (Subtype.property.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) q))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
@@ -652,7 +652,7 @@ theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
 lean 3 declaration is
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 but is expected to have type
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Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (a : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x) f))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_symm_apply Submodule.coe_isComplEquivProj_symm_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_symm_apply (f : { f : E →ₗ[R] p // ∀ x : p, f x = x }) :
@@ -724,7 +724,7 @@ def codRestrict {f : M →ₗ[S] M} (h : IsProj m f) : M →ₗ[S] m :=
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S M M (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)))))) f) (x : M), Eq.{succ u2} M ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) x m))))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) => M -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} S S M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) (LinearMap.IsProj.codRestrict.{u1, u2} S _inst_8 M _inst_9 _inst_10 m f h) x)) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) f x)
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) x) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f x)
+  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) x) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f x)
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply LinearMap.IsProj.codRestrict_applyₓ'. -/
 @[simp]
 theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.codRestrict x) = f x :=
@@ -735,7 +735,7 @@ theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.c
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S M M (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)))))) f) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) => M -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} S S M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) (LinearMap.IsProj.codRestrict.{u1, u2} S _inst_8 M _inst_9 _inst_10 m f h) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) x m))))) x)) x
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) x
+  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) x
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_codₓ'. -/
 @[simp]
 theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.codRestrict x = x :=
@@ -749,7 +749,7 @@ theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.c
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S M M (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)))))) f), Eq.{succ u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (LinearMap.ker.{u1, u1, u2, u2, u2} S S M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) (LinearMap.IsProj.codRestrict.{u1, u2} S _inst_8 M _inst_9 _inst_10 m f h)) (LinearMap.ker.{u1, u1, u2, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) f)
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f), Eq.{succ u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (LinearMap.ker.{u2, u2, u1, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h)) (LinearMap.ker.{u2, u2, u1, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f)
+  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f), Eq.{succ u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (LinearMap.ker.{u2, u2, u1, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h)) (LinearMap.ker.{u2, u2, u1, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f)
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_ker LinearMap.IsProj.codRestrict_kerₓ'. -/
 theorem codRestrict_ker {f : M →ₗ[S] M} (h : IsProj m f) : h.codRestrict.ker = f.ker :=
   f.ker_codRestrict m _
@@ -759,7 +759,7 @@ theorem codRestrict_ker {f : M →ₗ[S] M} (h : IsProj m f) : h.codRestrict.ker
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3}, (LinearMap.IsProj.{u1, u2, u2} R (Ring.toSemiring.{u1} R _inst_1) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R E E (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) f) -> (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p (LinearMap.ker.{u1, u1, u2, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3}, (LinearMap.IsProj.{u2, u1, u1} R (Ring.toSemiring.{u2} R _inst_1) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) -> (IsCompl.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3}, (LinearMap.IsProj.{u2, u1, u1} R (Ring.toSemiring.{u2} R _inst_1) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) -> (IsCompl.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.is_compl LinearMap.IsProj.isComplₓ'. -/
 theorem isCompl {f : E →ₗ[R] E} (h : IsProj p f) : IsCompl p f.ker :=
   by
@@ -771,7 +771,7 @@ theorem isCompl {f : E →ₗ[R] E} (h : IsProj p f) : IsCompl p f.ker :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u1, u2, u2} R (Ring.toSemiring.{u1} R _inst_1) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R E E (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) f), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) f (LinearMap.comp.{u1, u1, u1, u2, u2, u2} R R R E (Prod.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))) E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Prod.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ u2)} 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_inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.prodEquivOfIsCompl._proof_1.{u1} R _inst_1) (Submodule.prodEquivOfIsCompl._proof_2.{u1} R _inst_1) (Submodule.prodEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u1, u1, u2, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (LinearMap.IsProj.isCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f h))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u2, u1, u1} R (Ring.toSemiring.{u2} R _inst_1) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) 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(Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) 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(Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Submodule.prodEquivOfIsCompl.{u2, u1} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.IsProj.isCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f h))))))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u2, u1, u1} R (Ring.toSemiring.{u2} R _inst_1) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) f (LinearMap.comp.{u2, u2, u2, u1, u1, u1} R R R E (Prod.{u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)))) E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Prod.instAddCommMonoidSum.{u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} 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u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E 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R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Submodule.prodEquivOfIsCompl.{u2, u1} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.IsProj.isCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f h))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map' LinearMap.IsProj.eq_conj_prod_map'ₓ'. -/
 theorem eq_conj_prod_map' {f : E →ₗ[R] E} (h : IsProj p f) :
     f =
@@ -808,7 +808,7 @@ variable {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E] {p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u1, u2, u2} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R E E (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) f), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) f (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearEquiv.conj._proof_3.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearEquiv.conj._proof_4.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Module.End.{u1, u2} R (Prod.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R 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(CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u2, u1, u1} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f))) (LinearMap.instZeroLinearMap.{u2, u2, u1, u1} R R (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u2, u1, u1} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map LinearMap.IsProj.eq_conj_prodMapₓ'. -/
 theorem IsProj.eq_conj_prodMap {f : E →ₗ[R] E} (h : IsProj p f) :
     f = (p.prodEquivOfIsCompl f.ker h.IsCompl).conj (prodMap id 0) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -487,7 +487,7 @@ theorem ofIsCompl_add (h : IsCompl p q) {φ₁ φ₂ : p →ₗ[R] F} {ψ₁ ψ
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_11 : CommRing.{u1} R] {E : Type.{u2}} [_inst_12 : AddCommGroup.{u2} E] [_inst_13 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12)] {F : Type.{u3}} [_inst_14 : AddCommGroup.{u3} F] [_inst_15 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) p q) {φ : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) p) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15} {ψ : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) q) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15} (c : R), Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_13 _inst_15) (LinearMap.ofIsCompl.{u1, u2, u3} R (CommRing.toRing.{u1} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h (SMul.smul.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) p) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15) (LinearMap.hasSmul.{u1, u1, u1, u2, u3} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) p) F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Module.toDistribMulAction.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15) (smulCommClass_self.{u1, u3} R F (CommRing.toCommMonoid.{u1} R _inst_11) (MulActionWithZero.toMulAction.{u1, u3} R F (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_14)))) (Module.toMulActionWithZero.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15)))) c φ) (SMul.smul.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) q) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (LinearMap.hasSmul.{u1, u1, u1, u2, u3} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) q) F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Module.toDistribMulAction.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15) (smulCommClass_self.{u1, u3} R F (CommRing.toCommMonoid.{u1} R _inst_11) (MulActionWithZero.toMulAction.{u1, u3} R F (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_14)))) (Module.toMulActionWithZero.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15)))) c ψ)) (SMul.smul.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_13 _inst_15) (LinearMap.hasSmul.{u1, u1, u1, u2, u3} R R R E F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_13 _inst_15 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Module.toDistribMulAction.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15) (smulCommClass_self.{u1, u3} R F (CommRing.toCommMonoid.{u1} R _inst_11) (MulActionWithZero.toMulAction.{u1, u3} R F (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_14)))) (Module.toMulActionWithZero.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15)))) c (LinearMap.ofIsCompl.{u1, u2, u3} R (CommRing.toRing.{u1} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h φ ψ))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_11 : CommRing.{u3} R] {E : Type.{u2}} [_inst_12 : AddCommGroup.{u2} E] [_inst_13 : Module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12)] {F : Type.{u1}} [_inst_14 : AddCommGroup.{u1} F] [_inst_15 : Module.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14)] {p : Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} {q : Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} (h : IsCompl.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (Submodule.completeLattice.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (Submodule.completeLattice.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) p q) {φ : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15} {ψ : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15} (c : R), Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.ofIsCompl.{u3, u2, u1} R (CommRing.toRing.{u3} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15) (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E 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(CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c φ) (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (instHSMul.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c ψ)) (HSMul.hSMul.{u3, max u1 u2, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (instHSMul.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R E F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c (LinearMap.ofIsCompl.{u3, u2, u1} R (CommRing.toRing.{u3} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h φ ψ))
+  forall {R : Type.{u3}} [_inst_11 : CommRing.{u3} R] {E : Type.{u2}} [_inst_12 : AddCommGroup.{u2} E] [_inst_13 : Module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12)] {F : Type.{u1}} [_inst_14 : AddCommGroup.{u1} F] [_inst_15 : Module.{u3, u1} R F (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14)] {p : Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} {q : Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} (h : IsCompl.{u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (Submodule.completeLattice.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (Submodule.completeLattice.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) p q) {φ : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15} {ψ : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15} (c : R), Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.ofIsCompl.{u3, u2, u1} R (CommRing.toRing.{u3} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15) (instHSMul.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c φ) (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (instHSMul.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (Submodule.addCommMonoid.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c ψ)) (HSMul.hSMul.{u3, max u1 u2, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (instHSMul.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R E F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c (LinearMap.ofIsCompl.{u3, u2, u1} R (CommRing.toRing.{u3} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h φ ψ))
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_smul LinearMap.ofIsCompl_smulₓ'. -/
 @[simp]
 theorem ofIsCompl_smul {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E]
@@ -504,7 +504,7 @@ variable {R₁ : Type _} [CommRing R₁] [Module R₁ E] [Module R₁ F]
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.partialOrder.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearMap.{u3, u3, max u1 u2, max u1 u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) 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(RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_1.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_2.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_3.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearMap.{u3, u3, max u2 u1, max u2 u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Prod.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E 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(Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))))
+  forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearMap.{u3, u3, max u2 u1, max u2 u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Prod.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13)) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ E F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (Prod.module.{u3, max u1 u2, max u1 u2} R₁ (LinearMap.{u3, u3, u1, u2} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) 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(CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod LinearMap.ofIsComplProdₓ'. -/
 /-- The linear map from `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` to `E →ₗ[R₁] F`. -/
 def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
@@ -523,7 +523,7 @@ def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} (h : IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.partialOrder.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ 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 but is expected to have type
-  forall {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_13 : Module.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} {q : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} (h : IsCompl.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) p q) (φ : Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ 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(CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13))))) (Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E 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(Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (Prod.module.{u3, max u2 u1, max u2 u1} R₁ (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) 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(CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u2, u1, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u2, u1} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ))
+  forall {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_13 : Module.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} {q : Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} (h : IsCompl.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) p q) (φ : Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ 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(CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) 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F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ E F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u2, u1, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u2, u1} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ))
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_applyₓ'. -/
 @[simp]
 theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
@@ -535,7 +535,7 @@ theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.partialOrder.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearEquiv.{u3, u3, max u1 u2, max u1 u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (LinearMap.ofIsComplProdEquiv._proof_1.{u3} R₁ _inst_11) (LinearMap.ofIsComplProdEquiv._proof_2.{u3} R₁ _inst_11) (Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) 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_inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProdEquiv._proof_3.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProdEquiv._proof_4.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProdEquiv._proof_5.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearEquiv.{u3, u3, max u2 u1, max u2 u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (RingHomInvPair.ids.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (RingHomInvPair.ids.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (Prod.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13)) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (Prod.module.{u3, max u1 u2, max u1 u2} R₁ (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))))
+  forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearEquiv.{u3, u3, max u2 u1, max u2 u1} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (RingHomInvPair.ids.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (RingHomInvPair.ids.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (Prod.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ 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(CommRing.toCommSemiring.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)))) (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_equiv LinearMap.ofIsComplProdEquivₓ'. -/
 /-- The natural linear equivalence between `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` and `E →ₗ[R₁] F`. -/
 def ofIsComplProdEquiv {p q : Submodule R₁ E} (h : IsCompl p q) :
@@ -808,7 +808,7 @@ variable {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E] {p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u1, u2, u2} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R E E (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) f), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) f (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearEquiv.conj._proof_3.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearEquiv.conj._proof_4.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Module.End.{u1, u2} R (Prod.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R 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_inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u2, u1, u1} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) f), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E 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(CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) f))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) f)) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) f)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u2, u1, u1} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.End.{u2, u1} R (Prod.{u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) 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=> Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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(Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f))))))))))) (SMulZeroClass.toSMul.{u2, u1} R (Module.End.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (AddMonoid.toZero.{u1} (Module.End.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{u1} (Module.End.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (Module.End.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (AddMonoid.toAddZeroClass.{u1} (Module.End.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (AddCommMonoid.toAddMonoid.{u1} (Module.End.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, u1} R (Module.End.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Module.End.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R (Module.End.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R E (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R E (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2))) (Module.toMulActionWithZero.{u2, u1} R E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u2, u1, u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.End.{u2, u1} R (Prod.{u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Prod.instAddCommMonoidSum.{u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) 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(CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) 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(LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) f)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map LinearMap.IsProj.eq_conj_prodMapₓ'. -/
 theorem IsProj.eq_conj_prodMap {f : E →ₗ[R] E} (h : IsProj p f) :
     f = (p.prodEquivOfIsCompl f.ker h.IsCompl).conj (prodMap id 0) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

@@ -51,7 +51,7 @@ open Submodule
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)}, (forall (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => E -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HSub.hSub.{u2, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (instHSub.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.hasSub.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_2 _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (LinearMap.id.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} R R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.subtype.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) f))) p)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)}, (forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun 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 Case conversion may be inaccurate. Consider using '#align linear_map.ker_id_sub_eq_of_proj LinearMap.ker_id_sub_eq_of_projₓ'. -/
 theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
     ker (id - p.Subtype.comp f) = p := by
@@ -64,7 +64,7 @@ theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) 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_inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E 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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) x) -> (Eq.{succ u1} (Submodule.{u2, u1} R (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align linear_map.range_eq_of_proj LinearMap.range_eq_of_projₓ'. -/
 theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f = ⊤ :=
   range_eq_top.2 fun x => ⟨x, hf x⟩
@@ -74,7 +74,7 @@ theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f
 lean 3 declaration is
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 but is expected to have type
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(CompleteLattice.toBoundedOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)}, (forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) x) -> (IsCompl.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
 Case conversion may be inaccurate. Consider using '#align linear_map.is_compl_of_proj LinearMap.isCompl_of_projₓ'. -/
 theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl p f.ker :=
   by
@@ -100,7 +100,7 @@ open LinearMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotientEquivOfIsCompl._proof_1.{u1} R _inst_1) (Submodule.quotientEquivOfIsCompl._proof_2.{u1} R _inst_1) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q))
 Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl Submodule.quotientEquivOfIsComplₓ'. -/
 /-- If `q` is a complement of `p`, then `M/p ≃ q`. -/
 def quotientEquivOfIsCompl (h : IsCompl p q) : (E ⧸ p) ≃ₗ[R] q :=
@@ -114,7 +114,7 @@ def quotientEquivOfIsCompl (h : IsCompl p q) : (E ⧸ p) ≃ₗ[R] q :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotientEquivOfIsCompl._proof_2.{u1} R _inst_1) (Submodule.quotientEquivOfIsCompl._proof_1.{u1} R _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) 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 but is expected to have type
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_inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.quotientEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) x) (Submodule.Quotient.mk.{u1, u2} R E _inst_1 _inst_2 _inst_3 p (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.quotientEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) x) (Submodule.Quotient.mk.{u1, u2} R E _inst_1 _inst_2 _inst_3 p (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x))
 Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl_symm_apply Submodule.quotientEquivOfIsCompl_symm_applyₓ'. -/
 @[simp]
 theorem quotientEquivOfIsCompl_symm_apply (h : IsCompl p q) (x : q) :
@@ -126,7 +126,7 @@ theorem quotientEquivOfIsCompl_symm_apply (h : IsCompl p q) (x : q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotientEquivOfIsCompl._proof_1.{u1} R _inst_1) (Submodule.quotientEquivOfIsCompl._proof_2.{u1} R _inst_1) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (fun (_x : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotientEquivOfIsCompl._proof_1.{u1} R _inst_1) (Submodule.quotientEquivOfIsCompl._proof_2.{u1} R _inst_1) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) 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 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x))) x
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Submodule.Quotient.mk.{u1, u2} R E _inst_1 _inst_2 _inst_3 p (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x))) (FunLike.coe.{succ u2, succ u2, succ 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(Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (SMulZeroClass.toSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddMonoid.toZero.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)))) (DistribSMul.toSMulZeroClass.{u1, u2} R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)))) (DistribMulAction.toDistribSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p))) (Module.toDistribMulAction.{u1, u2} R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p))))) 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, 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(HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Submodule.quotientEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Submodule.Quotient.mk.{u1, u2} R E _inst_1 _inst_2 _inst_3 p (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x))) x
 Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl_apply_mk_coe Submodule.quotientEquivOfIsCompl_apply_mk_coeₓ'. -/
 @[simp]
 theorem quotientEquivOfIsCompl_apply_mk_coe (h : IsCompl p q) (x : q) :
@@ -138,7 +138,7 @@ theorem quotientEquivOfIsCompl_apply_mk_coe (h : IsCompl p q) (x : q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R E _inst_1 _inst_2 _inst_3 p ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) E (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) E (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) E (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) E (coeSubtype.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q))))) (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotientEquivOfIsCompl._proof_1.{u1} R _inst_1) (Submodule.quotientEquivOfIsCompl._proof_2.{u1} R _inst_1) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (fun (_x : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotientEquivOfIsCompl._proof_1.{u1} R _inst_1) (Submodule.quotientEquivOfIsCompl._proof_2.{u1} R _inst_1) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) => (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q)) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u2} R R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.quotientEquivOfIsCompl._proof_1.{u1} R _inst_1) (Submodule.quotientEquivOfIsCompl._proof_2.{u1} R _inst_1)) (Submodule.quotientEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x))) x
 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p), Eq.{succ u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.mk.{u1, u2} R E _inst_1 _inst_2 _inst_3 p (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (HasQuotient.Quotient.{u2, u2} E 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(Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} 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(Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)))) (DistribSMul.toSMulZeroClass.{u1, u2} R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddMonoid.toAddZeroClass.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddCommMonoid.toAddMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)))) (DistribMulAction.toDistribSMul.{u1, u2} R (HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R 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(HasQuotient.Quotient.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.hasQuotient.{u1, u2} R E _inst_1 _inst_2 _inst_3) p) (Submodule.Quotient.addCommGroup.{u1, u2} R E _inst_1 _inst_2 _inst_3 p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.Quotient.module.{u1, u2} R E _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Submodule.quotientEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x))) x
 Case conversion may be inaccurate. Consider using '#align submodule.mk_quotient_equiv_of_is_compl_apply Submodule.mk_quotientEquivOfIsCompl_applyₓ'. -/
 @[simp]
 theorem mk_quotientEquivOfIsCompl_apply (h : IsCompl p q) (x : E ⧸ p) :
@@ -150,7 +150,7 @@ theorem mk_quotientEquivOfIsCompl_apply (h : IsCompl p q) (x : E ⧸ p) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.prodEquivOfIsCompl._proof_1.{u1} R _inst_1) (Submodule.prodEquivOfIsCompl._proof_2.{u1} R _inst_1) (Prod.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q)) E (Prod.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Prod.module.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) _inst_3)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Prod.{u2, u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q))) E (Prod.instAddCommMonoidSum.{u2, u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Prod.module.{u1, u2, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) _inst_3)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Prod.{u2, u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q))) E (Prod.instAddCommMonoidSum.{u2, u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Prod.module.{u1, u2, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) _inst_3)
 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl Submodule.prodEquivOfIsComplₓ'. -/
 /-- If `q` is a complement of `p`, then `p × q` is isomorphic to `E`. It is the unique
 linear map `f : E → p` such that `f x = x` for `x ∈ p` and `f x = 0` for `x ∈ q`. -/
@@ -168,7 +168,7 @@ def prodEquivOfIsCompl (h : IsCompl p q) : (p × q) ≃ₗ[R] E :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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 but is expected to have type
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_inst_2) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_3 (Submodule.subtype.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.subtype.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Prod.{u2, u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q))) E (Prod.instAddCommMonoidSum.{u2, u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Prod.module.{u1, u2, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) _inst_3) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Prod.{u2, u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q))) E (Prod.instAddCommMonoidSum.{u2, u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Prod.module.{u1, u2, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) _inst_3 (Submodule.prodEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) (LinearMap.coprod.{u1, u2, u2, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) E (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_3 (Submodule.subtype.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.subtype.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_prod_equiv_of_is_compl Submodule.coe_prodEquivOfIsComplₓ'. -/
 @[simp]
 theorem coe_prodEquivOfIsCompl (h : IsCompl p q) :
@@ -180,7 +180,7 @@ theorem coe_prodEquivOfIsCompl (h : IsCompl p q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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 Case conversion may be inaccurate. Consider using '#align submodule.coe_prod_equiv_of_is_compl' Submodule.coe_prodEquivOfIsCompl'ₓ'. -/
 @[simp]
 theorem coe_prodEquivOfIsCompl' (h : IsCompl p q) (x : p × q) :
@@ -190,9 +190,9 @@ theorem coe_prodEquivOfIsCompl' (h : IsCompl p q) (x : p × q) :
 
 /- warning: submodule.prod_equiv_of_is_compl_symm_apply_left -> Submodule.prodEquivOfIsCompl_symm_apply_left is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_left Submodule.prodEquivOfIsCompl_symm_apply_leftₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_left (h : IsCompl p q) (x : p) :
@@ -202,9 +202,9 @@ theorem prodEquivOfIsCompl_symm_apply_left (h : IsCompl p q) (x : p) :
 
 /- warning: submodule.prod_equiv_of_is_compl_symm_apply_right -> Submodule.prodEquivOfIsCompl_symm_apply_right is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_right Submodule.prodEquivOfIsCompl_symm_apply_rightₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_right (h : IsCompl p q) (x : q) :
@@ -214,9 +214,9 @@ theorem prodEquivOfIsCompl_symm_apply_right (h : IsCompl p q) (x : q) :
 
 /- warning: submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero -> Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zeroₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
@@ -229,9 +229,9 @@ theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
 
 /- warning: submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero -> Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero is a dubious translation:
 lean 3 declaration is
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u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)
 Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zeroₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_snd_eq_zero (h : IsCompl p q) {x : E} :
@@ -246,7 +246,7 @@ theorem prodEquivOfIsCompl_symm_apply_snd_eq_zero (h : IsCompl p q) {x : E} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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E _inst_2 _inst_3 q p (IsCompl.symm.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q h))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Prod.{u2, u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R 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_inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q h))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (Prod.module.{u1, u2, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomCompTriple.ids.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.prodComm.{u1, u2, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (Submodule.prodEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) (Submodule.prodEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 q p (IsCompl.symm.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q h))
 Case conversion may be inaccurate. Consider using '#align submodule.prod_comm_trans_prod_equiv_of_is_compl Submodule.prodComm_trans_prodEquivOfIsComplₓ'. -/
 @[simp]
 theorem prodComm_trans_prodEquivOfIsCompl (h : IsCompl p q) :
@@ -258,7 +258,7 @@ theorem prodComm_trans_prodEquivOfIsCompl (h : IsCompl p q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl Submodule.linearProjOfIsComplₓ'. -/
 /-- Projection to a submodule along its complement. -/
 def linearProjOfIsCompl (h : IsCompl p q) : E →ₗ[R] p :=
@@ -271,7 +271,7 @@ variable {p q}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E 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E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_left Submodule.linearProjOfIsCompl_apply_leftₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_left (h : IsCompl p q) (x : p) :
@@ -282,7 +282,7 @@ theorem linearProjOfIsCompl_apply_left (h : IsCompl p q) (x : p) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (Submodule.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.range.{u1, u1, u2, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) (Top.top.{u2} (Submodule.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (Submodule.hasTop.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.range.{u1, u1, u2, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) 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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_range Submodule.linearProjOfIsCompl_rangeₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_range (h : IsCompl p q) : (linearProjOfIsCompl p q h).range = ⊤ :=
@@ -291,9 +291,9 @@ theorem linearProjOfIsCompl_range (h : IsCompl p q) : (linearProjOfIsCompl p q h
 
 /- warning: submodule.linear_proj_of_is_compl_apply_eq_zero_iff -> Submodule.linearProjOfIsCompl_apply_eq_zero_iff is a dubious translation:
 lean 3 declaration is
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(Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) {x : E}, Iff (Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} 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 but is expected to have type
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(Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))) (Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) {x : E}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) 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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_eq_zero_iff Submodule.linearProjOfIsCompl_apply_eq_zero_iffₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
@@ -302,9 +302,9 @@ theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
 
 /- warning: submodule.linear_proj_of_is_compl_apply_right' -> Submodule.linearProjOfIsCompl_apply_right' is a dubious translation:
 lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 0 (OfNat.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 0 (Zero.zero.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : E), (Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right' Submodule.linearProjOfIsCompl_apply_right'ₓ'. -/
 theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q) :
     linearProjOfIsCompl p q h x = 0 :=
@@ -313,9 +313,9 @@ theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q
 
 /- warning: submodule.linear_proj_of_is_compl_apply_right -> Submodule.linearProjOfIsCompl_apply_right is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) (Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E 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E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) (Submodule.zero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right Submodule.linearProjOfIsCompl_apply_rightₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_right (h : IsCompl p q) (x : q) :
@@ -327,7 +327,7 @@ theorem linearProjOfIsCompl_apply_right (h : IsCompl p q) (x : q) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) q
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) q
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h)) q
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_ker Submodule.linearProjOfIsCompl_kerₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_ker (h : IsCompl p q) : (linearProjOfIsCompl p q h).ker = q :=
@@ -338,7 +338,7 @@ theorem linearProjOfIsCompl_ker (h : IsCompl p q) : (linearProjOfIsCompl p q h).
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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 but is expected to have type
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p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} R R R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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(Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.ids.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Submodule.subtype.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.id.{u1, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} R R R 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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_comp_subtype Submodule.linearProjOfIsCompl_comp_subtypeₓ'. -/
 theorem linearProjOfIsCompl_comp_subtype (h : IsCompl p q) :
     (linearProjOfIsCompl p q h).comp p.Subtype = id :=
@@ -349,7 +349,7 @@ theorem linearProjOfIsCompl_comp_subtype (h : IsCompl p q) :
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_idempotent Submodule.linearProjOfIsCompl_idempotentₓ'. -/
 theorem linearProjOfIsCompl_idempotent (h : IsCompl p q) (x : E) :
     linearProjOfIsCompl p q h (linearProjOfIsCompl p q h x) = linearProjOfIsCompl p q h x :=
@@ -360,7 +360,7 @@ theorem linearProjOfIsCompl_idempotent (h : IsCompl p q) (x : E) :
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3}, (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) u))) x))
 Case conversion may be inaccurate. Consider using '#align submodule.exists_unique_add_of_is_compl_prod Submodule.existsUnique_add_of_isCompl_prodₓ'. -/
 theorem existsUnique_add_of_isCompl_prod (hc : IsCompl p q) (x : E) :
     ∃! u : p × q, (u.fst : E) + u.snd = x :=
@@ -371,7 +371,7 @@ theorem existsUnique_add_of_isCompl_prod (hc : IsCompl p q) (x : E) :
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3}, (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (forall (x : E), Exists.{succ u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (fun (u : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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 Case conversion may be inaccurate. Consider using '#align submodule.exists_unique_add_of_is_compl Submodule.existsUnique_add_of_isComplₓ'. -/
 theorem existsUnique_add_of_isCompl (hc : IsCompl p q) (x : E) :
     ∃ (u : p)(v : q), (u : E) + v = x ∧ ∀ (r : p) (s : q), (r : E) + s = x → r = u ∧ s = v :=
@@ -383,7 +383,7 @@ theorem existsUnique_add_of_isCompl (hc : IsCompl p q) (x : E) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (hpq : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q hpq)) x))) x
 but is expected to have type
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_inst_2) _inst_3 q) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 q p (IsCompl.symm.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q hpq)) x))) x
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (hpq : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : E), Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q hpq) x)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 q p (IsCompl.symm.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q hpq)) x))) x
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_add_linear_proj_of_is_compl_eq_self Submodule.linear_proj_add_linearProjOfIsCompl_eq_selfₓ'. -/
 theorem linear_proj_add_linearProjOfIsCompl_eq_self (hpq : IsCompl p q) (x : E) :
     (p.linearProjOfIsCompl q hpq x + q.linearProjOfIsCompl p hpq.symm x : E) = x :=
@@ -403,7 +403,7 @@ open Submodule
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3}, (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_5) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_5) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3}, (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_5) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_5) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3}, (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_5) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_5) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5)
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl LinearMap.ofIsComplₓ'. -/
 /-- Given linear maps `φ` and `ψ` from complement submodules, `of_is_compl` is
 the induced linear map over the entire module. -/
@@ -417,7 +417,7 @@ variable {p q}
 lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) => F) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) φ u)
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_left_apply LinearMap.ofIsCompl_left_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (u : p) :
@@ -428,7 +428,7 @@ theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →
 lean 3 declaration is
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 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) => F) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) ψ v)
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(Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5} {ψ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5} (v : Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => F) (Subtype.val.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Set.{u3} E) 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(LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) ψ v)
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_right_apply LinearMap.ofIsCompl_right_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (v : q) :
@@ -439,7 +439,7 @@ theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_eq LinearMap.ofIsCompl_eqₓ'. -/
 theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : ∀ u, φ u = χ u) (hψ : ∀ u, ψ u = χ u) : ofIsCompl h φ ψ = χ :=
@@ -453,7 +453,7 @@ theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) {φ : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_5} {ψ : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_5} {χ : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5}, (Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_5) φ (LinearMap.comp.{u1, u1, u1, u2, u2, u3} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) χ (Submodule.subtype.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))) -> (Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_5) ψ (LinearMap.comp.{u1, u1, u1, u2, u2, u3} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) χ (Submodule.subtype.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q))) -> (Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.ofIsCompl.{u1, u2, u3} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 p q h φ ψ) χ)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) p q) {φ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5} {ψ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5} {χ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5}, (Eq.{max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5) φ (LinearMap.comp.{u2, u2, u2, u3, u3, u1} R R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) E F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) χ (Submodule.subtype.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p))) -> (Eq.{max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5) ψ (LinearMap.comp.{u2, u2, u2, u3, u3, u1} R R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) E F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) χ (Submodule.subtype.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q))) -> (Eq.{max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (LinearMap.ofIsCompl.{u2, u3, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 p q h φ ψ) χ)
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) p q) {φ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5} {ψ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5} {χ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5}, (Eq.{max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5) φ (LinearMap.comp.{u2, u2, u2, u3, u3, u1} R R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) E F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) χ (Submodule.subtype.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p))) -> (Eq.{max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5) ψ (LinearMap.comp.{u2, u2, u2, u3, u3, u1} R R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) E F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomCompTriple.ids.{u2, u2} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) χ (Submodule.subtype.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q))) -> (Eq.{max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (LinearMap.ofIsCompl.{u2, u3, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 p q h φ ψ) χ)
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_eq' LinearMap.ofIsCompl_eq'ₓ'. -/
 theorem ofIsCompl_eq' (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : φ = χ.comp p.Subtype) (hψ : ψ = χ.comp q.Subtype) : ofIsCompl h φ ψ = χ :=
@@ -464,7 +464,7 @@ theorem ofIsCompl_eq' (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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 but is expected to have type
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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5) 0 (Zero.toOfNat0.{max u3 u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) 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_inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))))) (OfNat.ofNat.{max u3 u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) 0 (Zero.toOfNat0.{max u3 u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (LinearMap.instZeroLinearMap.{u2, u2, u3, u1} R R E F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) p q), Eq.{max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (LinearMap.ofIsCompl.{u2, u3, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 p q h (OfNat.ofNat.{max u3 u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R 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_inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5) 0 (Zero.toOfNat0.{max u3 u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5) (LinearMap.instZeroLinearMap.{u2, u2, u3, u1} R R (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} 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(AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) 0 (Zero.toOfNat0.{max u3 u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (LinearMap.instZeroLinearMap.{u2, u2, u3, u1} R R E F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_zero LinearMap.ofIsCompl_zeroₓ'. -/
 @[simp]
 theorem ofIsCompl_zero (h : IsCompl p q) : (ofIsCompl h 0 0 : E →ₗ[R] F) = 0 :=
@@ -475,7 +475,7 @@ theorem ofIsCompl_zero (h : IsCompl p q) : (ofIsCompl h 0 0 : E →ₗ[R] F) = 0
 lean 3 declaration is
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 but is expected to have type
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E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5} {ψ₂ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) 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(Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) ψ₁ ψ₂)) (HAdd.hAdd.{max u3 u1, max u3 u1, max u3 u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (instHAdd.{max u3 u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (LinearMap.instAddLinearMap.{u2, u2, u3, u1} R R E F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (LinearMap.ofIsCompl.{u2, u3, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 p q h φ₁ ψ₁) (LinearMap.ofIsCompl.{u2, u3, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 p q h φ₂ ψ₂))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) p q) {φ₁ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5} {φ₂ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5} {ψ₁ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5} {ψ₂ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) 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E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) φ₁ φ₂) (HAdd.hAdd.{max u3 u1, max u3 u1, max u3 u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E 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(Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) ψ₁ ψ₂)) (HAdd.hAdd.{max u3 u1, max u3 u1, max u3 u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (instHAdd.{max u3 u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) (LinearMap.instAddLinearMap.{u2, u2, u3, u1} R R E F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))))) (LinearMap.ofIsCompl.{u2, u3, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 p q h φ₁ ψ₁) (LinearMap.ofIsCompl.{u2, u3, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 p q h φ₂ ψ₂))
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_add LinearMap.ofIsCompl_addₓ'. -/
 @[simp]
 theorem ofIsCompl_add (h : IsCompl p q) {φ₁ φ₂ : p →ₗ[R] F} {ψ₁ ψ₂ : q →ₗ[R] F} :
@@ -487,7 +487,7 @@ theorem ofIsCompl_add (h : IsCompl p q) {φ₁ φ₂ : p →ₗ[R] F} {ψ₁ ψ
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_11 : CommRing.{u1} R] {E : Type.{u2}} [_inst_12 : AddCommGroup.{u2} E] [_inst_13 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12)] {F : Type.{u3}} [_inst_14 : AddCommGroup.{u3} F] [_inst_15 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) 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Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) p) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15} {ψ : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) q) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15} (c : R), Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_13 _inst_15) (LinearMap.ofIsCompl.{u1, u2, u3} R (CommRing.toRing.{u1} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h (SMul.smul.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) p) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15) (LinearMap.hasSmul.{u1, u1, u1, u2, u3} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) p) F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Module.toDistribMulAction.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15) (smulCommClass_self.{u1, u3} R F (CommRing.toCommMonoid.{u1} R _inst_11) (MulActionWithZero.toMulAction.{u1, u3} R F (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_14)))) (Module.toMulActionWithZero.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15)))) c φ) (SMul.smul.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) q) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (LinearMap.hasSmul.{u1, u1, u1, u2, u3} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) q) F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Module.toDistribMulAction.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15) (smulCommClass_self.{u1, u3} R F (CommRing.toCommMonoid.{u1} R _inst_11) (MulActionWithZero.toMulAction.{u1, u3} R F (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_14)))) (Module.toMulActionWithZero.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15)))) c ψ)) (SMul.smul.{u1, max u2 u3} R (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_13 _inst_15) (LinearMap.hasSmul.{u1, u1, u1, u2, u3} R R R E F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_13 _inst_15 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)))) (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_11)) (Module.toDistribMulAction.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15) (smulCommClass_self.{u1, u3} R F (CommRing.toCommMonoid.{u1} R _inst_11) (MulActionWithZero.toMulAction.{u1, u3} R F (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_14)))) (Module.toMulActionWithZero.{u1, u3} R F (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_14) _inst_15)))) c (LinearMap.ofIsCompl.{u1, u2, u3} R (CommRing.toRing.{u1} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h φ ψ))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_11 : CommRing.{u3} R] {E : Type.{u2}} [_inst_12 : AddCommGroup.{u2} E] [_inst_13 : Module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12)] {F : Type.{u1}} [_inst_14 : AddCommGroup.{u1} F] [_inst_15 : Module.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14)] {p : Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} {q : Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} (h : IsCompl.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (Submodule.completeLattice.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (Submodule.completeLattice.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) p q) {φ : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.instSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15} {ψ : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.instSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15} (c : R), Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.ofIsCompl.{u3, u2, u1} R (CommRing.toRing.{u3} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.instSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15) (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E 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(CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.instSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.instSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c φ) (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.instSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.instSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (instHSMul.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.instSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.instSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c ψ)) (HSMul.hSMul.{u3, max u1 u2, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (instHSMul.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R E F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c (LinearMap.ofIsCompl.{u3, u2, u1} R (CommRing.toRing.{u3} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h φ ψ))
+  forall {R : Type.{u3}} [_inst_11 : CommRing.{u3} R] {E : Type.{u2}} [_inst_12 : AddCommGroup.{u2} E] [_inst_13 : Module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12)] {F : Type.{u1}} [_inst_14 : AddCommGroup.{u1} F] [_inst_15 : Module.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14)] {p : Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} {q : Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} (h : IsCompl.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (Submodule.completeLattice.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (Submodule.completeLattice.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) p q) {φ : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15} {ψ : LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15} (c : R), Eq.{max (succ u2) (succ u1)} (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.ofIsCompl.{u3, u2, u1} R (CommRing.toRing.{u3} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => 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_inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c φ) (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (instHSMul.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.setLike.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x q)) F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Submodule.addCommMonoid.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c ψ)) (HSMul.hSMul.{u3, max u1 u2, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (instHSMul.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.instSMulLinearMap.{u3, u3, u3, u2, u1} R R R E F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c (LinearMap.ofIsCompl.{u3, u2, u1} R (CommRing.toRing.{u3} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h φ ψ))
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_smul LinearMap.ofIsCompl_smulₓ'. -/
 @[simp]
 theorem ofIsCompl_smul {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E]
@@ -504,7 +504,7 @@ variable {R₁ : Type _} [CommRing R₁] [Module R₁ E] [Module R₁ F]
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.partialOrder.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) 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(CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) 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_inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_1.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (coeSort.{succ u1, succ 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(Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_2.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_3.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearMap.{u3, u3, max u2 u1, max u2 u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ 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R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (Prod.module.{u3, max u1 u2, max u1 u2} R₁ (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))))
+  forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearMap.{u3, u3, max u2 u1, max u2 u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Prod.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E 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(Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod LinearMap.ofIsComplProdₓ'. -/
 /-- The linear map from `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` to `E →ₗ[R₁] F`. -/
 def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
@@ -523,7 +523,7 @@ def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} (h : IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.partialOrder.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ 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_inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F 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(Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_2.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_3.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u1, u2, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u1, u2} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) φ))
 but is expected to have type
-  forall {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_13 : Module.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} {q : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} (h : IsCompl.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ 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x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) 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(Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F 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(smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u2, u1, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u2, u1} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ))
+  forall {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_13 : Module.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} {q : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} (h : IsCompl.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) p q) (φ : Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) 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(CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13))))) (Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E 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(Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (Prod.module.{u3, max u2 u1, max u2 u1} R₁ (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) 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(CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u2, u1, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u2, u1} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ))
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_applyₓ'. -/
 @[simp]
 theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
@@ -535,7 +535,7 @@ theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.partialOrder.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearEquiv.{u3, u3, max u1 u2, max u1 u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) 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_inst_11))))) (Prod.module.{u3, max u1 u2, max u1 u2} R₁ (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProdEquiv._proof_3.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProdEquiv._proof_4.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProdEquiv._proof_5.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearEquiv.{u3, u3, max u2 u1, max u2 u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ 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_inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))))
+  forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearEquiv.{u3, u3, max u2 u1, max u2 u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (RingHomInvPair.ids.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (RingHomInvPair.ids.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (Prod.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13)) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13) (Prod.instAddCommMonoidSum.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (Prod.module.{u3, max u1 u2, max u1 u2} R₁ (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u2} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u2} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_equiv LinearMap.ofIsComplProdEquivₓ'. -/
 /-- The natural linear equivalence between `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` and `E →ₗ[R₁] F`. -/
 def ofIsComplProdEquiv {p q : Submodule R₁ E} (h : IsCompl p q) :
@@ -558,7 +558,7 @@ end
 lean 3 declaration is
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_inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.isCompl_of_proj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f hf)) f
 Case conversion may be inaccurate. Consider using '#align linear_map.linear_proj_of_is_compl_of_proj LinearMap.linearProjOfIsCompl_of_projₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x) :
@@ -624,7 +624,7 @@ open LinearMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), Equiv.{succ u2, succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q)) (Subtype.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R 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_inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => forall (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => E -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (coeSubtype.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p))))) x)) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), Equiv.{succ u2, succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) 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(LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), Equiv.{succ u2, succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q)) (Subtype.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (fun (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => forall (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E 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(Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x))
 Case conversion may be inaccurate. Consider using '#align submodule.is_compl_equiv_proj Submodule.isComplEquivProjₓ'. -/
 /-- Equivalence between submodules `q` such that `is_compl p q` and linear maps `f : E →ₗ[R] p`
 such that `∀ x : p, f x = x`. -/
@@ -640,7 +640,7 @@ def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p
 lean 3 declaration is
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(Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q))))) q) (Subtype.property.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R 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 but is expected to have type
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_inst_2) _inst_3) p)) x)) x))) (Submodule.isComplEquivProj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p) q)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p (Subtype.val.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) 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_inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) q))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
@@ -652,7 +652,7 @@ theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
 lean 3 declaration is
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_inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x)) (Submodule.isComplEquivProj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p)) f)) (LinearMap.ker.{u1, u1, u2, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Subtype.val.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (fun (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => forall (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (a : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x) f))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_symm_apply Submodule.coe_isComplEquivProj_symm_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_symm_apply (f : { f : E →ₗ[R] p // ∀ x : p, f x = x }) :
@@ -711,7 +711,7 @@ variable {p m}
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10}, (LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S M M (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)))))) f) -> (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m))
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10}, (LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) f) -> (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u1, u2} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} S M _inst_8 _inst_9 _inst_10 m))
+  forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10}, (LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) f) -> (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m))
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict LinearMap.IsProj.codRestrictₓ'. -/
 /-- Restriction of the codomain of a projection of onto a subspace `p` to `p` instead of the whole
 space.
@@ -724,7 +724,7 @@ def codRestrict {f : M →ₗ[S] M} (h : IsProj m f) : M →ₗ[S] m :=
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S M M (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)))))) f) (x : M), Eq.{succ u2} M ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) x m))))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) => M -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} S S M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) (LinearMap.IsProj.codRestrict.{u1, u2} S _inst_8 M _inst_9 _inst_10 m f h) x)) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) f x)
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) x) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f x)
+  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) x) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f x)
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply LinearMap.IsProj.codRestrict_applyₓ'. -/
 @[simp]
 theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.codRestrict x) = f x :=
@@ -735,7 +735,7 @@ theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.c
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S M M (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)))))) f) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) => M -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} S S M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) (LinearMap.IsProj.codRestrict.{u1, u2} S _inst_8 M _inst_9 _inst_10 m f h) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) x m))))) x)) x
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) x
+  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) x
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_codₓ'. -/
 @[simp]
 theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.codRestrict x = x :=
@@ -749,7 +749,7 @@ theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.c
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S M M (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)))))) f), Eq.{succ u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (LinearMap.ker.{u1, u1, u2, u2, u2} S S M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) (LinearMap.IsProj.codRestrict.{u1, u2} S _inst_8 M _inst_9 _inst_10 m f h)) (LinearMap.ker.{u1, u1, u2, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) f)
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f), Eq.{succ u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (LinearMap.ker.{u2, u2, u1, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h)) (LinearMap.ker.{u2, u2, u1, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f)
+  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f), Eq.{succ u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (LinearMap.ker.{u2, u2, u1, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h)) (LinearMap.ker.{u2, u2, u1, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f)
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_ker LinearMap.IsProj.codRestrict_kerₓ'. -/
 theorem codRestrict_ker {f : M →ₗ[S] M} (h : IsProj m f) : h.codRestrict.ker = f.ker :=
   f.ker_codRestrict m _
@@ -771,7 +771,7 @@ theorem isCompl {f : E →ₗ[R] E} (h : IsProj p f) : IsCompl p f.ker :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u1, u2, u2} R (Ring.toSemiring.{u1} R _inst_1) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R E E (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) f), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) f (LinearMap.comp.{u1, u1, u1, u2, u2, u2} R R R E (Prod.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))) E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Prod.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ u2)} 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_inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Submodule.prodEquivOfIsCompl._proof_1.{u1} R _inst_1) (Submodule.prodEquivOfIsCompl._proof_2.{u1} R _inst_1) (Submodule.prodEquivOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u1, u1, u2, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (LinearMap.IsProj.isCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f h))))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u2, u1, u1} R (Ring.toSemiring.{u2} R _inst_1) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Submodule.prodEquivOfIsCompl.{u2, u1} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.IsProj.isCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f h))))))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u2, u1, u1} R (Ring.toSemiring.{u2} R _inst_1) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) f (LinearMap.comp.{u2, u2, u2, u1, u1, u1} R R R E (Prod.{u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)))) E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Prod.instAddCommMonoidSum.{u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u2, u1} R E 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(Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))) (LinearEquiv.symm.{u2, u2, u1, u1} R R (Prod.{u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Prod.module.{u2, u1, u1} R (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (Submodule.addCommMonoid.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (Submodule.module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Submodule.prodEquivOfIsCompl.{u2, u1} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.IsProj.isCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f h))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map' LinearMap.IsProj.eq_conj_prod_map'ₓ'. -/
 theorem eq_conj_prod_map' {f : E →ₗ[R] E} (h : IsProj p f) :
     f =
@@ -808,7 +808,7 @@ variable {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E] {p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u1, u2, u2} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u1, u2} R E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u2} R E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) R E E (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Module.toDistribMulAction.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R E E (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) f), Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) f (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearEquiv.conj._proof_3.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearEquiv.conj._proof_4.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Module.End.{u1, u2} R (Prod.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R 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(CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R E E (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))))
 but is expected to have type
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(Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E 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(Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) f))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) 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(CommRing.toRing.{u2} R _inst_1))))) f)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) f)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) f)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3} (h : LinearMap.IsProj.{u2, u1, u1} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) f), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Module.End.{u2, u1} R (Prod.{u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.setLike.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) 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 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map LinearMap.IsProj.eq_conj_prodMapₓ'. -/
 theorem IsProj.eq_conj_prodMap {f : E →ₗ[R] E} (h : IsProj p f) :
     f = (p.prodEquivOfIsCompl f.ker h.IsCompl).conj (prodMap id 0) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -51,7 +51,7 @@ open Submodule
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) 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(Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HSub.hSub.{u1, u1, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E 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(Ring.toSemiring.{u2} R _inst_1))))) (LinearMap.id.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (LinearMap.comp.{u2, u2, u2, u1, u1, u1} R R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) 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 Case conversion may be inaccurate. Consider using '#align linear_map.ker_id_sub_eq_of_proj LinearMap.ker_id_sub_eq_of_projₓ'. -/
 theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
     ker (id - p.Subtype.comp f) = p := by
@@ -64,7 +64,7 @@ theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align linear_map.range_eq_of_proj LinearMap.range_eq_of_projₓ'. -/
 theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f = ⊤ :=
   range_eq_top.2 fun x => ⟨x, hf x⟩
@@ -74,7 +74,7 @@ theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f
 lean 3 declaration is
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 but is expected to have type
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(CompleteLattice.toBoundedOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E 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(Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) 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 Case conversion may be inaccurate. Consider using '#align linear_map.is_compl_of_proj LinearMap.isCompl_of_projₓ'. -/
 theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl p f.ker :=
   by
@@ -271,7 +271,7 @@ variable {p q}
 lean 3 declaration is
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(SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (coeSubtype.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p))))) x)) x
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_left Submodule.linearProjOfIsCompl_apply_leftₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_left (h : IsCompl p q) (x : p) :
@@ -293,7 +293,7 @@ theorem linearProjOfIsCompl_range (h : IsCompl p q) : (linearProjOfIsCompl p q h
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) {x : E}, Iff (Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} 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 but is expected to have type
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(Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))) (Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) {x : E}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) 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Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))) (Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_eq_zero_iff Submodule.linearProjOfIsCompl_apply_eq_zero_iffₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
@@ -304,7 +304,7 @@ theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : E), (Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q) -> (Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 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(Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => E -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p q h) x) (OfNat.ofNat.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 0 (OfNat.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) 0 (Zero.zero.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Submodule.hasZero.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))))
 but is expected to have type
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(x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) x) (Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : E), (Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right' Submodule.linearProjOfIsCompl_apply_right'ₓ'. -/
 theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q) :
     linearProjOfIsCompl p q h x = 0 :=
@@ -315,7 +315,7 @@ theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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_inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) q)) x)) (Submodule.instZeroSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)))
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right Submodule.linearProjOfIsCompl_apply_rightₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_right (h : IsCompl p q) (x : q) :
@@ -349,7 +349,7 @@ theorem linearProjOfIsCompl_comp_subtype (h : IsCompl p q) :
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_idempotent Submodule.linearProjOfIsCompl_idempotentₓ'. -/
 theorem linearProjOfIsCompl_idempotent (h : IsCompl p q) (x : E) :
     linearProjOfIsCompl p q h (linearProjOfIsCompl p q h x) = linearProjOfIsCompl p q h x :=
@@ -383,7 +383,7 @@ theorem existsUnique_add_of_isCompl (hc : IsCompl p q) (x : E) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (hpq : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 q p (IsCompl.symm.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q hpq)) x))) x
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (hpq : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : E), Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) (FunLike.coe.{succ u2, succ u2, 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_inst_2) _inst_3 q) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 q p (IsCompl.symm.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q hpq)) x))) x
 Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_add_linear_proj_of_is_compl_eq_self Submodule.linear_proj_add_linearProjOfIsCompl_eq_selfₓ'. -/
 theorem linear_proj_add_linearProjOfIsCompl_eq_self (hpq : IsCompl p q) (x : E) :
     (p.linearProjOfIsCompl q hpq x + q.linearProjOfIsCompl p hpq.symm x : E) = x :=
@@ -417,7 +417,7 @@ variable {p q}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) p q) {φ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5} {ψ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) 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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_left_apply LinearMap.ofIsCompl_left_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (u : p) :
@@ -428,7 +428,7 @@ theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) p q) {φ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5} {ψ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) 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(Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x q)) F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 q) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) ψ v)
 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_right_apply LinearMap.ofIsCompl_right_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (v : q) :
@@ -439,7 +439,7 @@ theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) 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_inst_2) _inst_3 q) _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) ψ u) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u1} R R E F (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) χ (Subtype.val.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Set.{u3} E) 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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_eq LinearMap.ofIsCompl_eqₓ'. -/
 theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : ∀ u, φ u = χ u) (hψ : ∀ u, ψ u = χ u) : ofIsCompl h φ ψ = χ :=
@@ -523,7 +523,7 @@ def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} (h : IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.partialOrder.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ 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(CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F 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_inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_1.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (coeSort.{succ u1, succ 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(Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_2.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_3.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u1, u2, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u1, u2} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) φ))
 but is expected to have type
-  forall {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_13 : Module.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} {q : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} (h : IsCompl.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) p q) (φ : Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ 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x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) 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(Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ))
+  forall {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_13 : Module.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} {q : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} (h : IsCompl.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) p q) (φ : Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ 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_inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ 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_inst_12) E (Submodule.instSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E 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(SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (smulCommClass_self.{u3, u1} R₁ F (CommRing.toCommMonoid.{u3} R₁ _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R₁ F (Semiring.toMonoidWithZero.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_4))))) (Module.toMulActionWithZero.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) _inst_13)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u2, u1, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u2, u1} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E 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_inst_12) E (Submodule.instSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ 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 Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_applyₓ'. -/
 @[simp]
 theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
@@ -558,7 +558,7 @@ end
 lean 3 declaration is
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+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (hf : forall (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) p)) x)) x), Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (Submodule.linearProjOfIsCompl.{u2, u1} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.isCompl_of_proj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f hf)) f
 Case conversion may be inaccurate. Consider using '#align linear_map.linear_proj_of_is_compl_of_proj LinearMap.linearProjOfIsCompl_of_projₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x) :
@@ -605,7 +605,7 @@ theorem coe_equivProdOfSurjectiveOfIsCompl {f : E →ₗ[R] F} {g : E →ₗ[R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {G : Type.{u4}} [_inst_6 : AddCommGroup.{u4} G] [_inst_7 : Module.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6)] {f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5} {g : LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7} (hf : Eq.{succ u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f) (Top.top.{u3} (Submodule.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5) (Submodule.hasTop.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_5))) (hg : Eq.{succ u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (LinearMap.range.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g) (Top.top.{u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (Submodule.hasTop.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7))) (hfg : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) 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 but is expected to have type
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+  forall {R : Type.{u4}} [_inst_1 : Ring.{u4} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u4, u3} R E (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] [_inst_5 : Module.{u4, u2} R F (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {G : Type.{u1}} [_inst_6 : AddCommGroup.{u1} G] [_inst_7 : Module.{u4, u1} R G (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6)] {f : LinearMap.{u4, u4, u3, u2} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5} {g : LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R 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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u2} R R E F (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) f x) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (LinearMap.{u4, u4, u3, u1} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => G) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, u1} R R E G (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) g x))
 Case conversion may be inaccurate. Consider using '#align linear_map.equiv_prod_of_surjective_of_is_compl_apply LinearMap.equivProdOfSurjectiveOfIsCompl_applyₓ'. -/
 @[simp]
 theorem equivProdOfSurjectiveOfIsCompl_apply {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
@@ -624,7 +624,7 @@ open LinearMap
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), Equiv.{succ u2, succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q)) (Subtype.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R 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_inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => forall (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) => E -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R E (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) E (coeSubtype.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p))))) x)) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), Equiv.{succ u2, succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q)) (Subtype.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) (fun (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3), Equiv.{succ u2, succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q)) (Subtype.{succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x))
 Case conversion may be inaccurate. Consider using '#align submodule.is_compl_equiv_proj Submodule.isComplEquivProjₓ'. -/
 /-- Equivalence between submodules `q` such that `is_compl p q` and linear maps `f : E →ₗ[R] p`
 such that `∀ x : p, f x = x`. -/
@@ -640,7 +640,7 @@ def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p
 lean 3 declaration is
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(Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q))))) q) (Subtype.property.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R 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 but is expected to have type
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q) q) (Subtype.property.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) 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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Subtype.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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(Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x))) (Submodule.isComplEquivProj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p) q)) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p (Subtype.val.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) q) (Subtype.property.{succ u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (fun (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) => IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) q))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
@@ -652,7 +652,7 @@ theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
 lean 3 declaration is
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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p)) E (fun (a : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R E (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) p)) x)) x) f))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_symm_apply Submodule.coe_isComplEquivProj_symm_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_symm_apply (f : { f : E →ₗ[R] p // ∀ x : p, f x = x }) :
@@ -724,7 +724,7 @@ def codRestrict {f : M →ₗ[S] M} (h : IsProj m f) : M →ₗ[S] m :=
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S M M (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)))))) f) (x : M), Eq.{succ u2} M ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) x m))))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) => M -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} S S M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_8 _inst_8 _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) (LinearMap.IsProj.codRestrict.{u1, u2} S _inst_8 M _inst_9 _inst_10 m f h) x)) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8))) f x)
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M) x) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f x)
+  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : M), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) x) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f x)
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply LinearMap.IsProj.codRestrict_applyₓ'. -/
 @[simp]
 theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.codRestrict x) = f x :=
@@ -735,7 +735,7 @@ theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.c
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_8 : Semiring.{u1} S] {M : Type.{u2}} [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} S M _inst_8 _inst_9] {m : Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u1, u2, u2} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (SMulZeroClass.toHasSmul.{u1, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9))) (DistribSMul.toSmulZeroClass.{u1, u2} S M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_9)) (DistribMulAction.toDistribSMul.{u1, u2} S M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10)))) (DistribMulActionHomClass.toSmulHomClass.{u2, u1, u2, u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) S M M (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S _inst_8)) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (AddCommMonoid.toAddMonoid.{u2} M _inst_9) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (Module.toDistribMulAction.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} S M M (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (LinearMap.semilinearMapClass.{u1, u1, u2, u2} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)))))) f) (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) _inst_9 (Submodule.addCommMonoid.{u1, u2} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.module.{u1, u2} S M _inst_8 _inst_9 _inst_10 m)) (fun (_x : LinearMap.{u1, u1, u2, u2} S S _inst_8 _inst_8 (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S _inst_8)) M (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} 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(Semiring.toNonAssocSemiring.{u1} S _inst_8))) (LinearMap.IsProj.codRestrict.{u1, u2} S _inst_8 M _inst_9 _inst_10 m f h) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) m) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} S M _inst_8 _inst_9 _inst_10) M (Submodule.setLike.{u1, u2} S M _inst_8 _inst_9 _inst_10)) x m))))) x)) x
 but is expected to have type
-  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) x
+  forall {S : Type.{u2}} [_inst_8 : Semiring.{u2} S] {M : Type.{u1}} [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} S M _inst_8 _inst_9] {m : Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10} {f : LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10} (h : LinearMap.IsProj.{u2, u1, u1} S _inst_8 M _inst_9 _inst_10 m (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M M _inst_9 _inst_9 _inst_10 _inst_10) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M M _inst_8 _inst_8 _inst_9 _inst_9 _inst_10 _inst_10 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) f) (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} S S _inst_8 _inst_8 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8)) M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} S S M (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10)) x m)) _inst_8 _inst_8 _inst_9 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) _inst_10 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10 m) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_8))) (LinearMap.IsProj.codRestrict.{u2, u1} S _inst_8 M _inst_9 _inst_10 m f h) (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x (SetLike.coe.{u1, u1} (Submodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) M (Submodule.instSetLikeSubmodule.{u2, u1} S M _inst_8 _inst_9 _inst_10) m)) x)) x
 Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_codₓ'. -/
 @[simp]
 theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.codRestrict x = x :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module linear_algebra.projection
-! leanprover-community/mathlib commit 6d584f1709bedbed9175bd9350df46599bdd7213
+! leanprover-community/mathlib commit 3dadefa3f544b1db6214777fe47910739b54c66a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.LinearAlgebra.Prod
 /-!
 # Projection to a subspace
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define
 * `linear_proj_of_is_compl (p q : submodule R E) (h : is_compl p q)`: the projection of a module `E`
   to a submodule `p` along its complement `q`; it is the unique linear map `f : E → p` such that

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

@@ -44,6 +44,12 @@ variable {p}
 
 open Submodule
 
+/- warning: linear_map.ker_id_sub_eq_of_proj -> LinearMap.ker_id_sub_eq_of_proj is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_map.ker_id_sub_eq_of_proj LinearMap.ker_id_sub_eq_of_projₓ'. -/
 theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
     ker (id - p.Subtype.comp f) = p := by
   ext x
@@ -51,10 +57,22 @@ theorem ker_id_sub_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) :
   exact ⟨fun h => h.symm ▸ Submodule.coe_mem _, fun hx => by erw [hf ⟨x, hx⟩, Subtype.coe_mk]⟩
 #align linear_map.ker_id_sub_eq_of_proj LinearMap.ker_id_sub_eq_of_proj
 
+/- warning: linear_map.range_eq_of_proj -> LinearMap.range_eq_of_proj is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.range_eq_of_proj LinearMap.range_eq_of_projₓ'. -/
 theorem range_eq_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : range f = ⊤ :=
   range_eq_top.2 fun x => ⟨x, hf x⟩
 #align linear_map.range_eq_of_proj LinearMap.range_eq_of_proj
 
+/- warning: linear_map.is_compl_of_proj -> LinearMap.isCompl_of_proj is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.is_compl_of_proj LinearMap.isCompl_of_projₓ'. -/
 theorem isCompl_of_proj {f : E →ₗ[R] p} (hf : ∀ x : p, f x = x) : IsCompl p f.ker :=
   by
   constructor
@@ -75,6 +93,12 @@ namespace Submodule
 
 open LinearMap
 
+/- warning: submodule.quotient_equiv_of_is_compl -> Submodule.quotientEquivOfIsCompl is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl Submodule.quotientEquivOfIsComplₓ'. -/
 /-- If `q` is a complement of `p`, then `M/p ≃ q`. -/
 def quotientEquivOfIsCompl (h : IsCompl p q) : (E ⧸ p) ≃ₗ[R] q :=
   LinearEquiv.symm <|
@@ -83,24 +107,48 @@ def quotientEquivOfIsCompl (h : IsCompl p q) : (E ⧸ p) ≃ₗ[R] q :=
         rw [← range_eq_top, range_comp, range_subtype, map_mkq_eq_top, h.sup_eq_top]⟩
 #align submodule.quotient_equiv_of_is_compl Submodule.quotientEquivOfIsCompl
 
+/- warning: submodule.quotient_equiv_of_is_compl_symm_apply -> Submodule.quotientEquivOfIsCompl_symm_apply is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl_symm_apply Submodule.quotientEquivOfIsCompl_symm_applyₓ'. -/
 @[simp]
 theorem quotientEquivOfIsCompl_symm_apply (h : IsCompl p q) (x : q) :
     (quotientEquivOfIsCompl p q h).symm x = Quotient.mk x :=
   rfl
 #align submodule.quotient_equiv_of_is_compl_symm_apply Submodule.quotientEquivOfIsCompl_symm_apply
 
+/- warning: submodule.quotient_equiv_of_is_compl_apply_mk_coe -> Submodule.quotientEquivOfIsCompl_apply_mk_coe is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.quotient_equiv_of_is_compl_apply_mk_coe Submodule.quotientEquivOfIsCompl_apply_mk_coeₓ'. -/
 @[simp]
 theorem quotientEquivOfIsCompl_apply_mk_coe (h : IsCompl p q) (x : q) :
     quotientEquivOfIsCompl p q h (Quotient.mk x) = x :=
   (quotientEquivOfIsCompl p q h).apply_symm_apply x
 #align submodule.quotient_equiv_of_is_compl_apply_mk_coe Submodule.quotientEquivOfIsCompl_apply_mk_coe
 
+/- warning: submodule.mk_quotient_equiv_of_is_compl_apply -> Submodule.mk_quotientEquivOfIsCompl_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.mk_quotient_equiv_of_is_compl_apply Submodule.mk_quotientEquivOfIsCompl_applyₓ'. -/
 @[simp]
 theorem mk_quotientEquivOfIsCompl_apply (h : IsCompl p q) (x : E ⧸ p) :
     (Quotient.mk (quotientEquivOfIsCompl p q h x) : E ⧸ p) = x :=
   (quotientEquivOfIsCompl p q h).symm_apply_apply x
 #align submodule.mk_quotient_equiv_of_is_compl_apply Submodule.mk_quotientEquivOfIsCompl_apply
 
+/- warning: submodule.prod_equiv_of_is_compl -> Submodule.prodEquivOfIsCompl is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl Submodule.prodEquivOfIsComplₓ'. -/
 /-- If `q` is a complement of `p`, then `p × q` is isomorphic to `E`. It is the unique
 linear map `f : E → p` such that `f x = x` for `x ∈ p` and `f x = 0` for `x ∈ q`. -/
 def prodEquivOfIsCompl (h : IsCompl p q) : (p × q) ≃ₗ[R] E :=
@@ -113,30 +161,60 @@ def prodEquivOfIsCompl (h : IsCompl p q) : (p × q) ≃ₗ[R] E :=
   · rw [← range_eq_top, ← sup_eq_range, h.sup_eq_top]
 #align submodule.prod_equiv_of_is_compl Submodule.prodEquivOfIsCompl
 
+/- warning: submodule.coe_prod_equiv_of_is_compl -> Submodule.coe_prodEquivOfIsCompl is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.coe_prod_equiv_of_is_compl Submodule.coe_prodEquivOfIsComplₓ'. -/
 @[simp]
 theorem coe_prodEquivOfIsCompl (h : IsCompl p q) :
     (prodEquivOfIsCompl p q h : p × q →ₗ[R] E) = p.Subtype.coprod q.Subtype :=
   rfl
 #align submodule.coe_prod_equiv_of_is_compl Submodule.coe_prodEquivOfIsCompl
 
+/- warning: submodule.coe_prod_equiv_of_is_compl' -> Submodule.coe_prodEquivOfIsCompl' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align submodule.coe_prod_equiv_of_is_compl' Submodule.coe_prodEquivOfIsCompl'ₓ'. -/
 @[simp]
-theorem coe_prod_equiv_of_is_compl' (h : IsCompl p q) (x : p × q) :
+theorem coe_prodEquivOfIsCompl' (h : IsCompl p q) (x : p × q) :
     prodEquivOfIsCompl p q h x = x.1 + x.2 :=
   rfl
-#align submodule.coe_prod_equiv_of_is_compl' Submodule.coe_prod_equiv_of_is_compl'
-
+#align submodule.coe_prod_equiv_of_is_compl' Submodule.coe_prodEquivOfIsCompl'
+
+/- warning: submodule.prod_equiv_of_is_compl_symm_apply_left -> Submodule.prodEquivOfIsCompl_symm_apply_left is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) (x : Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : E) => Prod.{u2, u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q)) _inst_3 (Prod.module.{u1, u2, u2} R (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E 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+Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_left Submodule.prodEquivOfIsCompl_symm_apply_leftₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_left (h : IsCompl p q) (x : p) :
     (prodEquivOfIsCompl p q h).symm x = (x, 0) :=
   (prodEquivOfIsCompl p q h).symm_apply_eq.2 <| by simp
 #align submodule.prod_equiv_of_is_compl_symm_apply_left Submodule.prodEquivOfIsCompl_symm_apply_left
 
+/- warning: submodule.prod_equiv_of_is_compl_symm_apply_right -> Submodule.prodEquivOfIsCompl_symm_apply_right is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_right Submodule.prodEquivOfIsCompl_symm_apply_rightₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_right (h : IsCompl p q) (x : q) :
     (prodEquivOfIsCompl p q h).symm x = (0, x) :=
   (prodEquivOfIsCompl p q h).symm_apply_eq.2 <| by simp
 #align submodule.prod_equiv_of_is_compl_symm_apply_right Submodule.prodEquivOfIsCompl_symm_apply_right
 
+/- warning: submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero -> Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (h : IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) {x : E}, Iff (Eq.{succ u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) (Prod.fst.{u2, u2} (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) 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+Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zeroₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
     ((prodEquivOfIsCompl p q h).symm x).1 = 0 ↔ x ∈ q :=
@@ -146,6 +224,12 @@ theorem prodEquivOfIsCompl_symm_apply_fst_eq_zero (h : IsCompl p q) {x : E} :
     mem_right_iff_eq_zero_of_disjoint h.disjoint]
 #align submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero
 
+/- warning: submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero -> Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zeroₓ'. -/
 @[simp]
 theorem prodEquivOfIsCompl_symm_apply_snd_eq_zero (h : IsCompl p q) {x : E} :
     ((prodEquivOfIsCompl p q h).symm x).2 = 0 ↔ x ∈ p :=
@@ -155,12 +239,24 @@ theorem prodEquivOfIsCompl_symm_apply_snd_eq_zero (h : IsCompl p q) {x : E} :
     mem_left_iff_eq_zero_of_disjoint h.disjoint]
 #align submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.prod_comm_trans_prod_equiv_of_is_compl Submodule.prodComm_trans_prodEquivOfIsComplₓ'. -/
 @[simp]
 theorem prodComm_trans_prodEquivOfIsCompl (h : IsCompl p q) :
     LinearEquiv.prodComm R q p ≪≫ₗ prodEquivOfIsCompl p q h = prodEquivOfIsCompl q p h.symm :=
   LinearEquiv.ext fun _ => add_comm _ _
 #align submodule.prod_comm_trans_prod_equiv_of_is_compl Submodule.prodComm_trans_prodEquivOfIsCompl
 
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+Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl Submodule.linearProjOfIsComplₓ'. -/
 /-- Projection to a submodule along its complement. -/
 def linearProjOfIsCompl (h : IsCompl p q) : E →ₗ[R] p :=
   LinearMap.fst R p q ∘ₗ ↑(prodEquivOfIsCompl p q h).symm
@@ -168,58 +264,124 @@ def linearProjOfIsCompl (h : IsCompl p q) : E →ₗ[R] p :=
 
 variable {p q}
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_left Submodule.linearProjOfIsCompl_apply_leftₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_left (h : IsCompl p q) (x : p) :
     linearProjOfIsCompl p q h x = x := by simp [linear_proj_of_is_compl]
 #align submodule.linear_proj_of_is_compl_apply_left Submodule.linearProjOfIsCompl_apply_left
 
+/- warning: submodule.linear_proj_of_is_compl_range -> Submodule.linearProjOfIsCompl_range is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_range Submodule.linearProjOfIsCompl_rangeₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_range (h : IsCompl p q) : (linearProjOfIsCompl p q h).range = ⊤ :=
   range_eq_of_proj (linearProjOfIsCompl_apply_left h)
 #align submodule.linear_proj_of_is_compl_range Submodule.linearProjOfIsCompl_range
 
+/- warning: submodule.linear_proj_of_is_compl_apply_eq_zero_iff -> Submodule.linearProjOfIsCompl_apply_eq_zero_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_eq_zero_iff Submodule.linearProjOfIsCompl_apply_eq_zero_iffₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_eq_zero_iff (h : IsCompl p q) {x : E} :
     linearProjOfIsCompl p q h x = 0 ↔ x ∈ q := by simp [linear_proj_of_is_compl]
 #align submodule.linear_proj_of_is_compl_apply_eq_zero_iff Submodule.linearProjOfIsCompl_apply_eq_zero_iff
 
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+Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right' Submodule.linearProjOfIsCompl_apply_right'ₓ'. -/
 theorem linearProjOfIsCompl_apply_right' (h : IsCompl p q) (x : E) (hx : x ∈ q) :
     linearProjOfIsCompl p q h x = 0 :=
   (linearProjOfIsCompl_apply_eq_zero_iff h).2 hx
 #align submodule.linear_proj_of_is_compl_apply_right' Submodule.linearProjOfIsCompl_apply_right'
 
+/- warning: submodule.linear_proj_of_is_compl_apply_right -> Submodule.linearProjOfIsCompl_apply_right is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_apply_right Submodule.linearProjOfIsCompl_apply_rightₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_apply_right (h : IsCompl p q) (x : q) :
     linearProjOfIsCompl p q h x = 0 :=
   linearProjOfIsCompl_apply_right' h x x.2
 #align submodule.linear_proj_of_is_compl_apply_right Submodule.linearProjOfIsCompl_apply_right
 
+/- warning: submodule.linear_proj_of_is_compl_ker -> Submodule.linearProjOfIsCompl_ker is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_ker Submodule.linearProjOfIsCompl_kerₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_ker (h : IsCompl p q) : (linearProjOfIsCompl p q h).ker = q :=
   ext fun x => mem_ker.trans (linearProjOfIsCompl_apply_eq_zero_iff h)
 #align submodule.linear_proj_of_is_compl_ker Submodule.linearProjOfIsCompl_ker
 
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+Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_comp_subtype Submodule.linearProjOfIsCompl_comp_subtypeₓ'. -/
 theorem linearProjOfIsCompl_comp_subtype (h : IsCompl p q) :
     (linearProjOfIsCompl p q h).comp p.Subtype = id :=
   LinearMap.ext <| linearProjOfIsCompl_apply_left h
 #align submodule.linear_proj_of_is_compl_comp_subtype Submodule.linearProjOfIsCompl_comp_subtype
 
+/- warning: submodule.linear_proj_of_is_compl_idempotent -> Submodule.linearProjOfIsCompl_idempotent is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_of_is_compl_idempotent Submodule.linearProjOfIsCompl_idempotentₓ'. -/
 theorem linearProjOfIsCompl_idempotent (h : IsCompl p q) (x : E) :
     linearProjOfIsCompl p q h (linearProjOfIsCompl p q h x) = linearProjOfIsCompl p q h x :=
   linearProjOfIsCompl_apply_left h _
 #align submodule.linear_proj_of_is_compl_idempotent Submodule.linearProjOfIsCompl_idempotent
 
+/- warning: submodule.exists_unique_add_of_is_compl_prod -> Submodule.existsUnique_add_of_isCompl_prod is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align submodule.exists_unique_add_of_is_compl_prod Submodule.existsUnique_add_of_isCompl_prodₓ'. -/
 theorem existsUnique_add_of_isCompl_prod (hc : IsCompl p q) (x : E) :
     ∃! u : p × q, (u.fst : E) + u.snd = x :=
   (prodEquivOfIsCompl _ _ hc).toEquiv.Bijective.ExistsUnique _
 #align submodule.exists_unique_add_of_is_compl_prod Submodule.existsUnique_add_of_isCompl_prod
 
-theorem exists_unique_add_of_isCompl (hc : IsCompl p q) (x : E) :
+/- warning: submodule.exists_unique_add_of_is_compl -> Submodule.existsUnique_add_of_isCompl is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.exists_unique_add_of_is_compl Submodule.existsUnique_add_of_isComplₓ'. -/
+theorem existsUnique_add_of_isCompl (hc : IsCompl p q) (x : E) :
     ∃ (u : p)(v : q), (u : E) + v = x ∧ ∀ (r : p) (s : q), (r : E) + s = x → r = u ∧ s = v :=
   let ⟨u, hu₁, hu₂⟩ := existsUnique_add_of_isCompl_prod hc x
   ⟨u.1, u.2, hu₁, fun r s hrs => Prod.eq_iff_fst_eq_snd_eq.1 (hu₂ ⟨r, s⟩ hrs)⟩
-#align submodule.exists_unique_add_of_is_compl Submodule.exists_unique_add_of_isCompl
-
+#align submodule.exists_unique_add_of_is_compl Submodule.existsUnique_add_of_isCompl
+
+/- warning: submodule.linear_proj_add_linear_proj_of_is_compl_eq_self -> Submodule.linear_proj_add_linearProjOfIsCompl_eq_self is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_2) _inst_3 q) _inst_3 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Submodule.linearProjOfIsCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 q p (IsCompl.symm.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q hpq)) x))) x
+Case conversion may be inaccurate. Consider using '#align submodule.linear_proj_add_linear_proj_of_is_compl_eq_self Submodule.linear_proj_add_linearProjOfIsCompl_eq_selfₓ'. -/
 theorem linear_proj_add_linearProjOfIsCompl_eq_self (hpq : IsCompl p q) (x : E) :
     (p.linearProjOfIsCompl q hpq x + q.linearProjOfIsCompl p hpq.symm x : E) = x :=
   by
@@ -234,6 +396,12 @@ namespace LinearMap
 
 open Submodule
 
+/- warning: linear_map.of_is_compl -> LinearMap.ofIsCompl is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3}, (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_5) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.setLike.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) q) F (Submodule.addCommMonoid.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_5) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u3} R F (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4)] {p : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3} {q : Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3}, (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) p q) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 p) _inst_5) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 q) _inst_5) -> (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5)
+Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl LinearMap.ofIsComplₓ'. -/
 /-- Given linear maps `φ` and `ψ` from complement submodules, `of_is_compl` is
 the induced linear map over the entire module. -/
 def ofIsCompl {p q : Submodule R E} (h : IsCompl p q) (φ : p →ₗ[R] F) (ψ : q →ₗ[R] F) : E →ₗ[R] F :=
@@ -242,16 +410,34 @@ def ofIsCompl {p q : Submodule R E} (h : IsCompl p q) (φ : p →ₗ[R] F) (ψ :
 
 variable {p q}
 
+/- warning: linear_map.of_is_compl_left_apply -> LinearMap.ofIsCompl_left_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_left_apply LinearMap.ofIsCompl_left_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_left_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (u : p) :
     ofIsCompl h φ ψ (u : E) = φ u := by simp [of_is_compl]
 #align linear_map.of_is_compl_left_apply LinearMap.ofIsCompl_left_apply
 
+/- warning: linear_map.of_is_compl_right_apply -> LinearMap.ofIsCompl_right_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_right_apply LinearMap.ofIsCompl_right_applyₓ'. -/
 @[simp]
 theorem ofIsCompl_right_apply (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} (v : q) :
     ofIsCompl h φ ψ (v : E) = ψ v := by simp [of_is_compl]
 #align linear_map.of_is_compl_right_apply LinearMap.ofIsCompl_right_apply
 
+/- warning: linear_map.of_is_compl_eq -> LinearMap.ofIsCompl_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_eq LinearMap.ofIsCompl_eqₓ'. -/
 theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : ∀ u, φ u = χ u) (hψ : ∀ u, ψ u = χ u) : ofIsCompl h φ ψ = χ :=
   by
@@ -260,22 +446,46 @@ theorem ofIsCompl_eq (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F}
   simp [of_is_compl, hφ, hψ]
 #align linear_map.of_is_compl_eq LinearMap.ofIsCompl_eq
 
+/- warning: linear_map.of_is_compl_eq' -> LinearMap.ofIsCompl_eq' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u3}} [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : Module.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] [_inst_5 : Module.{u2, u1} R F (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} {q : Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3} (h : IsCompl.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) 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(Submodule.instSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3 p) _inst_5} {ψ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) 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+Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_eq' LinearMap.ofIsCompl_eq'ₓ'. -/
 theorem ofIsCompl_eq' (h : IsCompl p q) {φ : p →ₗ[R] F} {ψ : q →ₗ[R] F} {χ : E →ₗ[R] F}
     (hφ : φ = χ.comp p.Subtype) (hψ : ψ = χ.comp q.Subtype) : ofIsCompl h φ ψ = χ :=
   ofIsCompl_eq h (fun _ => hφ.symm ▸ rfl) fun _ => hψ.symm ▸ rfl
 #align linear_map.of_is_compl_eq' LinearMap.ofIsCompl_eq'
 
+/- warning: linear_map.of_is_compl_zero -> LinearMap.ofIsCompl_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_zero LinearMap.ofIsCompl_zeroₓ'. -/
 @[simp]
 theorem ofIsCompl_zero (h : IsCompl p q) : (ofIsCompl h 0 0 : E →ₗ[R] F) = 0 :=
   ofIsCompl_eq _ (fun _ => rfl) fun _ => rfl
 #align linear_map.of_is_compl_zero LinearMap.ofIsCompl_zero
 
+/- warning: linear_map.of_is_compl_add -> LinearMap.ofIsCompl_add is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3)) p q) {φ₁ : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Subtype.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_3) E 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_inst_2 _inst_3 F _inst_4 _inst_5 p q h φ₁ ψ₁) (LinearMap.ofIsCompl.{u2, u3, u1} R _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 p q h φ₂ ψ₂))
+Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_add LinearMap.ofIsCompl_addₓ'. -/
 @[simp]
 theorem ofIsCompl_add (h : IsCompl p q) {φ₁ φ₂ : p →ₗ[R] F} {ψ₁ ψ₂ : q →ₗ[R] F} :
     ofIsCompl h (φ₁ + φ₂) (ψ₁ + ψ₂) = ofIsCompl h φ₁ ψ₁ + ofIsCompl h φ₂ ψ₂ :=
   ofIsCompl_eq _ (by simp) (by simp)
 #align linear_map.of_is_compl_add LinearMap.ofIsCompl_add
 
+/- warning: linear_map.of_is_compl_smul -> LinearMap.ofIsCompl_smul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u3}} [_inst_11 : CommRing.{u3} R] {E : Type.{u2}} [_inst_12 : AddCommGroup.{u2} E] [_inst_13 : Module.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12)] {F : Type.{u1}} [_inst_14 : AddCommGroup.{u1} F] [_inst_15 : Module.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14)] {p : Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} {q : Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13} (h : IsCompl.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R 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(CommRing.toRing.{u3} R _inst_11)))) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13) E (Submodule.instSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13)) x p)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R E (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R 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(AddCommGroup.toAddCommMonoid.{u2} E _inst_12) _inst_13 q) _inst_15 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) (Module.toDistribMulAction.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15) (smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c ψ)) (HSMul.hSMul.{u3, max u1 u2, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_12) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_13 _inst_15) (instHSMul.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) 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(smulCommClass_self.{u3, u1} R F (CommRing.toCommMonoid.{u3} R _inst_11) (MulActionWithZero.toMulAction.{u3, u1} R F (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_14))))) (Module.toMulActionWithZero.{u3, u1} R F (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_14) _inst_15))))) c (LinearMap.ofIsCompl.{u3, u2, u1} R (CommRing.toRing.{u3} R _inst_11) E _inst_12 _inst_13 F _inst_14 _inst_15 p q h φ ψ))
+Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_smul LinearMap.ofIsCompl_smulₓ'. -/
 @[simp]
 theorem ofIsCompl_smul {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E]
     {F : Type _} [AddCommGroup F] [Module R F] {p q : Submodule R E} (h : IsCompl p q)
@@ -287,6 +497,12 @@ section
 
 variable {R₁ : Type _} [CommRing R₁] [Module R₁ E] [Module R₁ F]
 
+/- warning: linear_map.of_is_compl_prod -> LinearMap.ofIsComplProd is a dubious translation:
+lean 3 declaration is
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_inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (LinearMap.addCommMonoid.{u3, u3, u1, u2} R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ 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(Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_2.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_3.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearMap.{u3, u3, max u2 u1, max u2 u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ 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(Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13)) (LinearMap.{u3, u3, u1, u2} R₁ R₁ 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(SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_4))))) (Module.toMulActionWithZero.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_13)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.instSetLikeSubmodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) x q)) F 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+Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod LinearMap.ofIsComplProdₓ'. -/
 /-- The linear map from `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` to `E →ₗ[R₁] F`. -/
 def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
     (p →ₗ[R₁] F) × (q →ₗ[R₁] F) →ₗ[R₁] E →ₗ[R₁] F
@@ -300,12 +516,24 @@ def ofIsComplProd {p q : Submodule R₁ E} (h : IsCompl p q) :
     simp [Prod.smul_snd, Prod.smul_fst, of_is_compl_smul]
 #align linear_map.of_is_compl_prod LinearMap.ofIsComplProd
 
+/- warning: linear_map.of_is_compl_prod_apply -> LinearMap.ofIsComplProd_apply is a dubious translation:
+lean 3 declaration is
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(Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_2.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProd._proof_3.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.ofIsComplProd.{u1, u2, u3} E _inst_2 F _inst_4 R₁ _inst_11 _inst_12 _inst_13 p q h) φ) (LinearMap.ofIsCompl.{u3, u1, u2} R₁ (CommRing.toRing.{u3} R₁ _inst_11) E _inst_2 _inst_12 F _inst_4 _inst_13 p q h (Prod.fst.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) φ) (Prod.snd.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 p) _inst_13) (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13) φ))
+but is expected to have type
+  forall {E : Type.{u2}} [_inst_2 : AddCommGroup.{u2} E] {F : Type.{u1}} [_inst_4 : AddCommGroup.{u1} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_13 : Module.{u3, u1} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4)] {p : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} {q : Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12} (h : IsCompl.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12)) p q) (φ : Prod.{max u1 u2, max u1 u2} (LinearMap.{u3, u3, u2, u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ 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x p)) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) (AddCommGroup.toAddCommMonoid.{u1} F _inst_4) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_12 p) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))))) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R₁ R₁ (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Submodule.{u3, u2} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) 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+Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_applyₓ'. -/
 @[simp]
 theorem ofIsComplProd_apply {p q : Submodule R₁ E} (h : IsCompl p q)
     (φ : (p →ₗ[R₁] F) × (q →ₗ[R₁] F)) : ofIsComplProd h φ = ofIsCompl h φ.1 φ.2 :=
   rfl
 #align linear_map.of_is_compl_prod_apply LinearMap.ofIsComplProd_apply
 
+/- warning: linear_map.of_is_compl_prod_equiv -> LinearMap.ofIsComplProdEquiv is a dubious translation:
+lean 3 declaration is
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_inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProdEquiv._proof_3.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ (coeSort.{succ u1, succ (succ u1)} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) E (Submodule.setLike.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) q) F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Submodule.addCommMonoid.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) (Submodule.module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12 q) _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProdEquiv._proof_4.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13))) (LinearMap.module.{u3, u3, u3, u1, u2} R₁ R₁ R₁ E F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4) _inst_12 _inst_13 (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) _inst_13 (LinearMap.ofIsComplProdEquiv._proof_5.{u2, u3} F _inst_4 R₁ _inst_11 _inst_13)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] {F : Type.{u2}} [_inst_4 : AddCommGroup.{u2} F] {R₁ : Type.{u3}} [_inst_11 : CommRing.{u3} R₁] [_inst_12 : Module.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_13 : Module.{u3, u2} R₁ F (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u2} F _inst_4)] {p : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12} {q : Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12}, (IsCompl.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (Submodule.completeLattice.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12)) p q) -> (LinearEquiv.{u3, u3, max u2 u1, max u2 u1} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (RingHomInvPair.ids.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (RingHomInvPair.ids.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11))) (Prod.{max u2 u1, max u2 u1} (LinearMap.{u3, u3, u1, u2} R₁ R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (RingHom.id.{u3} R₁ (Semiring.toNonAssocSemiring.{u3} R₁ (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)))) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ (CommRing.toRing.{u3} R₁ _inst_11)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_12) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₁ E (Ring.toSemiring.{u3} R₁ 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+Case conversion may be inaccurate. Consider using '#align linear_map.of_is_compl_prod_equiv LinearMap.ofIsComplProdEquivₓ'. -/
 /-- The natural linear equivalence between `(p →ₗ[R₁] F) × (q →ₗ[R₁] F)` and `E →ₗ[R₁] F`. -/
 def ofIsComplProdEquiv {p q : Submodule R₁ E} (h : IsCompl p q) :
     ((p →ₗ[R₁] F) × (q →ₗ[R₁] F)) ≃ₗ[R₁] E →ₗ[R₁] F :=
@@ -323,6 +551,12 @@ def ofIsComplProdEquiv {p q : Submodule R₁ E} (h : IsCompl p q) :
 
 end
 
+/- warning: linear_map.linear_proj_of_is_compl_of_proj -> LinearMap.linearProjOfIsCompl_of_proj is a dubious translation:
+lean 3 declaration is
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_inst_2) _inst_3 p) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.isCompl_of_proj.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f hf)) f
+Case conversion may be inaccurate. Consider using '#align linear_map.linear_proj_of_is_compl_of_proj LinearMap.linearProjOfIsCompl_of_projₓ'. -/
 @[simp]
 theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x) :
     p.linearProjOfIsCompl f.ker (isCompl_of_proj hf) = f :=
@@ -333,6 +567,12 @@ theorem linearProjOfIsCompl_of_proj (f : E →ₗ[R] p) (hf : ∀ x : p, f x = x
   simp [hf]
 #align linear_map.linear_proj_of_is_compl_of_proj LinearMap.linearProjOfIsCompl_of_proj
 
+/- warning: linear_map.equiv_prod_of_surjective_of_is_compl -> LinearMap.equivProdOfSurjectiveOfIsCompl is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) g) (Top.top.{u4} (Submodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7) (Submodule.instTopSubmodule.{u1, u4} R G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_7))) -> (IsCompl.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u2} (Submodule.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R E (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R E F (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (LinearMap.ker.{u1, u1, u2, u4, max u2 u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) E G (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u4} R R E G (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) g)) -> (LinearEquiv.{u1, u1, u2, max u4 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) E (Prod.{u3, u4} F G) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Prod.instAddCommMonoidSum.{u3, u4} F G (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6)) _inst_3 (Prod.module.{u1, u3, u4} R F G (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_4) (AddCommGroup.toAddCommMonoid.{u4} G _inst_6) _inst_5 _inst_7))
+Case conversion may be inaccurate. Consider using '#align linear_map.equiv_prod_of_surjective_of_is_compl LinearMap.equivProdOfSurjectiveOfIsComplₓ'. -/
 /-- If `f : E →ₗ[R] F` and `g : E →ₗ[R] G` are two surjective linear maps and
 their kernels are complement of each other, then `x ↦ (f x, g x)` defines
 a linear equivalence `E ≃ₗ[R] F × G`. -/
@@ -345,6 +585,12 @@ def equivProdOfSurjectiveOfIsCompl (f : E →ₗ[R] F) (g : E →ₗ[R] G) (hf :
       simp [range_prod_eq hfg.sup_eq_top, *]⟩
 #align linear_map.equiv_prod_of_surjective_of_is_compl LinearMap.equivProdOfSurjectiveOfIsCompl
 
+/- warning: linear_map.coe_equiv_prod_of_surjective_of_is_compl -> LinearMap.coe_equivProdOfSurjectiveOfIsCompl is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_map.coe_equiv_prod_of_surjective_of_is_compl LinearMap.coe_equivProdOfSurjectiveOfIsComplₓ'. -/
 @[simp]
 theorem coe_equivProdOfSurjectiveOfIsCompl {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
     (hg : g.range = ⊤) (hfg : IsCompl f.ker g.ker) :
@@ -352,6 +598,12 @@ theorem coe_equivProdOfSurjectiveOfIsCompl {f : E →ₗ[R] F} {g : E →ₗ[R]
   rfl
 #align linear_map.coe_equiv_prod_of_surjective_of_is_compl LinearMap.coe_equivProdOfSurjectiveOfIsCompl
 
+/- warning: linear_map.equiv_prod_of_surjective_of_is_compl_apply -> LinearMap.equivProdOfSurjectiveOfIsCompl_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_map.equiv_prod_of_surjective_of_is_compl_apply LinearMap.equivProdOfSurjectiveOfIsCompl_applyₓ'. -/
 @[simp]
 theorem equivProdOfSurjectiveOfIsCompl_apply {f : E →ₗ[R] F} {g : E →ₗ[R] G} (hf : f.range = ⊤)
     (hg : g.range = ⊤) (hfg : IsCompl f.ker g.ker) (x : E) :
@@ -365,6 +617,12 @@ namespace Submodule
 
 open LinearMap
 
+/- warning: submodule.is_compl_equiv_proj -> Submodule.isComplEquivProj is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.is_compl_equiv_proj Submodule.isComplEquivProjₓ'. -/
 /-- Equivalence between submodules `q` such that `is_compl p q` and linear maps `f : E →ₗ[R] p`
 such that `∀ x : p, f x = x`. -/
 def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p, f x = x }
@@ -375,12 +633,24 @@ def isComplEquivProj : { q // IsCompl p q } ≃ { f : E →ₗ[R] p // ∀ x : p
   right_inv := fun ⟨f, hf⟩ => Subtype.eq <| f.linearProjOfIsCompl_of_proj hf
 #align submodule.is_compl_equiv_proj Submodule.isComplEquivProj
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_apply (q : { q // IsCompl p q }) :
     (p.isComplEquivProj q : E →ₗ[R] p) = linearProjOfIsCompl p q q.2 :=
   rfl
 #align submodule.coe_is_compl_equiv_proj_apply Submodule.coe_isComplEquivProj_apply
 
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+Case conversion may be inaccurate. Consider using '#align submodule.coe_is_compl_equiv_proj_symm_apply Submodule.coe_isComplEquivProj_symm_applyₓ'. -/
 @[simp]
 theorem coe_isComplEquivProj_symm_apply (f : { f : E →ₗ[R] p // ∀ x : p, f x = x }) :
     (p.isComplEquivProj.symm f : Submodule R E) = (f : E →ₗ[R] p).ker :=
@@ -393,6 +663,7 @@ namespace LinearMap
 
 open Submodule
 
+#print LinearMap.IsProj /-
 /--
 A linear endomorphism of a module `E` is a projection onto a submodule `p` if it sends every element
 of `E` to `p` and fixes every element of `p`.
@@ -403,7 +674,14 @@ structure IsProj {F : Type _} [FunLike F M fun _ => M] (f : F) : Prop where
   map_mem : ∀ x, f x ∈ m
   map_id : ∀ x ∈ m, f x = x
 #align linear_map.is_proj LinearMap.IsProj
+-/
 
+/- warning: linear_map.is_proj_iff_idempotent -> LinearMap.isProj_iff_idempotent is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_map.is_proj_iff_idempotent LinearMap.isProj_iff_idempotentₓ'. -/
 theorem isProj_iff_idempotent (f : M →ₗ[S] M) : (∃ p : Submodule S M, IsProj p f) ↔ f ∘ₗ f = f :=
   by
   constructor
@@ -426,6 +704,12 @@ namespace IsProj
 
 variable {p m}
 
+/- warning: linear_map.is_proj.cod_restrict -> LinearMap.IsProj.codRestrict is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict LinearMap.IsProj.codRestrictₓ'. -/
 /-- Restriction of the codomain of a projection of onto a subspace `p` to `p` instead of the whole
 space.
 -/
@@ -433,11 +717,23 @@ def codRestrict {f : M →ₗ[S] M} (h : IsProj m f) : M →ₗ[S] m :=
   f.codRestrict m h.map_mem
 #align linear_map.is_proj.cod_restrict LinearMap.IsProj.codRestrict
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply LinearMap.IsProj.codRestrict_applyₓ'. -/
 @[simp]
 theorem codRestrict_apply {f : M →ₗ[S] M} (h : IsProj m f) (x : M) : ↑(h.codRestrict x) = f x :=
   f.codRestrict_apply m x
 #align linear_map.is_proj.cod_restrict_apply LinearMap.IsProj.codRestrict_apply
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_codₓ'. -/
 @[simp]
 theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.codRestrict x = x :=
   by
@@ -446,16 +742,34 @@ theorem codRestrict_apply_cod {f : M →ₗ[S] M} (h : IsProj m f) (x : m) : h.c
   exact h.map_id x x.2
 #align linear_map.is_proj.cod_restrict_apply_cod LinearMap.IsProj.codRestrict_apply_cod
 
+/- warning: linear_map.is_proj.cod_restrict_ker -> LinearMap.IsProj.codRestrict_ker is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.cod_restrict_ker LinearMap.IsProj.codRestrict_kerₓ'. -/
 theorem codRestrict_ker {f : M →ₗ[S] M} (h : IsProj m f) : h.codRestrict.ker = f.ker :=
   f.ker_codRestrict m _
 #align linear_map.is_proj.cod_restrict_ker LinearMap.IsProj.codRestrict_ker
 
+/- warning: linear_map.is_proj.is_compl -> LinearMap.IsProj.isCompl is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] {E : Type.{u1}} [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {p : Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3} {f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3}, (LinearMap.IsProj.{u2, u1, u1} R (Ring.toSemiring.{u2} R _inst_1) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) -> (IsCompl.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))) (CompleteLattice.toBoundedOrder.{u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.is_compl LinearMap.IsProj.isComplₓ'. -/
 theorem isCompl {f : E →ₗ[R] E} (h : IsProj p f) : IsCompl p f.ker :=
   by
   rw [← cod_restrict_ker]
   exact is_compl_of_proj h.cod_restrict_apply_cod
 #align linear_map.is_proj.is_compl LinearMap.IsProj.isCompl
 
+/- warning: linear_map.is_proj.eq_conj_prod_map' -> LinearMap.IsProj.eq_conj_prod_map' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x p)) (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) E (Submodule.instSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) x (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R 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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Submodule.prodEquivOfIsCompl.{u2, u1} R _inst_1 E _inst_2 _inst_3 p (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f) (LinearMap.IsProj.isCompl.{u1, u2} R _inst_1 E _inst_2 _inst_3 p f h))))))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map' LinearMap.IsProj.eq_conj_prod_map'ₓ'. -/
 theorem eq_conj_prod_map' {f : E →ₗ[R] E} (h : IsProj p f) :
     f =
       (p.prodEquivOfIsCompl f.ker h.IsCompl).toLinearMap ∘ₗ
@@ -487,6 +801,12 @@ namespace LinearMap
 
 variable {R : Type _} [CommRing R] {E : Type _} [AddCommGroup E] [Module R E] {p : Submodule R E}
 
+/- warning: linear_map.is_proj.eq_conj_prod_map -> LinearMap.IsProj.eq_conj_prodMap is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) f)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) f)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (LinearMap.ker.{u2, u2, u1, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) E E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R E E (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) f)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_proj.eq_conj_prod_map LinearMap.IsProj.eq_conj_prodMapₓ'. -/
 theorem IsProj.eq_conj_prodMap {f : E →ₗ[R] E} (h : IsProj p f) :
     f = (p.prodEquivOfIsCompl f.ker h.IsCompl).conj (prodMap id 0) :=
   by