algebra.module.submodule.bilinear | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

6010cf52

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

ee05e9ce

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2019 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Eric Wieser
 -/
-import Mathbin.LinearAlgebra.Span
-import Mathbin.LinearAlgebra.BilinearMap
+import LinearAlgebra.Span
+import LinearAlgebra.BilinearMap
 
 #align_import algebra.module.submodule.bilinear from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"

ee05e9ce

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.module.submodule.bilinear
-! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Span
 import Mathbin.LinearAlgebra.BilinearMap
 
+#align_import algebra.module.submodule.bilinear from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
+
 /-!
 # Images of pairs of submodules under bilinear maps

ee05e9ce

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -56,19 +56,24 @@ def map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R
 #align submodule.map₂ Submodule.map₂
 -/
 
+#print Submodule.apply_mem_map₂ /-
 theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Submodule R M}
     {q : Submodule R N} (hm : m ∈ p) (hn : n ∈ q) : f m n ∈ map₂ f p q :=
   (le_iSup _ ⟨m, hm⟩ : _ ≤ map₂ f p q) ⟨n, hn, rfl⟩
 #align submodule.apply_mem_map₂ Submodule.apply_mem_map₂
+-/
 
+#print Submodule.map₂_le /-
 theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submodule R N}
     {r : Submodule R P} : map₂ f p q ≤ r ↔ ∀ m ∈ p, ∀ n ∈ q, f m n ∈ r :=
   ⟨fun H m hm n hn => H <| apply_mem_map₂ _ hm hn, fun H =>
     iSup_le fun ⟨m, hm⟩ => map_le_iff_le_comap.2 fun n hn => H m hm n hn⟩
 #align submodule.map₂_le Submodule.map₂_le
+-/
 
 variable (R)
 
+#print Submodule.map₂_span_span /-
 theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N) :
     map₂ f (span R s) (span R t) = span R (Set.image2 (fun m n => f m n) s t) :=
   by
@@ -90,37 +95,49 @@ theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N)
   · rw [span_le]; rintro _ ⟨a, b, ha, hb, rfl⟩
     exact apply_mem_map₂ _ (subset_span ha) (subset_span hb)
 #align submodule.map₂_span_span Submodule.map₂_span_span
+-/
 
 variable {R}
 
+#print Submodule.map₂_bot_right /-
 @[simp]
 theorem map₂_bot_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) : map₂ f p ⊥ = ⊥ :=
   eq_bot_iff.2 <|
     map₂_le.2 fun m hm n hn => by rw [Submodule.mem_bot] at hn ⊢; rw [hn, LinearMap.map_zero]
 #align submodule.map₂_bot_right Submodule.map₂_bot_right
+-/
 
+#print Submodule.map₂_bot_left /-
 @[simp]
 theorem map₂_bot_left (f : M →ₗ[R] N →ₗ[R] P) (q : Submodule R N) : map₂ f ⊥ q = ⊥ :=
   eq_bot_iff.2 <|
     map₂_le.2 fun m hm n hn => by rw [Submodule.mem_bot] at hm ⊢; rw [hm, LinearMap.map_zero₂]
 #align submodule.map₂_bot_left Submodule.map₂_bot_left
+-/
 
+#print Submodule.map₂_le_map₂ /-
 @[mono]
 theorem map₂_le_map₂ {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submodule R M} {q₁ q₂ : Submodule R N}
     (hp : p₁ ≤ p₂) (hq : q₁ ≤ q₂) : map₂ f p₁ q₁ ≤ map₂ f p₂ q₂ :=
   map₂_le.2 fun m hm n hn => apply_mem_map₂ _ (hp hm) (hq hn)
 #align submodule.map₂_le_map₂ Submodule.map₂_le_map₂
+-/
 
+#print Submodule.map₂_le_map₂_left /-
 theorem map₂_le_map₂_left {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submodule R M} {q : Submodule R N}
     (h : p₁ ≤ p₂) : map₂ f p₁ q ≤ map₂ f p₂ q :=
   map₂_le_map₂ h (le_refl q)
 #align submodule.map₂_le_map₂_left Submodule.map₂_le_map₂_left
+-/
 
+#print Submodule.map₂_le_map₂_right /-
 theorem map₂_le_map₂_right {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q₁ q₂ : Submodule R N}
     (h : q₁ ≤ q₂) : map₂ f p q₁ ≤ map₂ f p q₂ :=
   map₂_le_map₂ (le_refl p) h
 #align submodule.map₂_le_map₂_right Submodule.map₂_le_map₂_right
+-/
 
+#print Submodule.map₂_sup_right /-
 theorem map₂_sup_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q₁ q₂ : Submodule R N) :
     map₂ f p (q₁ ⊔ q₂) = map₂ f p q₁ ⊔ map₂ f p q₂ :=
   le_antisymm
@@ -129,7 +146,9 @@ theorem map₂_sup_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q
       mem_sup.2 ⟨_, apply_mem_map₂ _ hm hn, _, apply_mem_map₂ _ hm hp, hnp ▸ (map_add _ _ _).symm⟩)
     (sup_le (map₂_le_map₂_right le_sup_left) (map₂_le_map₂_right le_sup_right))
 #align submodule.map₂_sup_right Submodule.map₂_sup_right
+-/
 
+#print Submodule.map₂_sup_left /-
 theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R M) (q : Submodule R N) :
     map₂ f (p₁ ⊔ p₂) q = map₂ f p₁ q ⊔ map₂ f p₂ q :=
   le_antisymm
@@ -140,22 +159,30 @@ theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R
           hmn ▸ (LinearMap.map_add₂ _ _ _ _).symm⟩)
     (sup_le (map₂_le_map₂_left le_sup_left) (map₂_le_map₂_left le_sup_right))
 #align submodule.map₂_sup_left Submodule.map₂_sup_left
+-/
 
+#print Submodule.image2_subset_map₂ /-
 theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     Set.image2 (fun m n => f m n) (↑p : Set M) (↑q : Set N) ⊆ (↑(map₂ f p q) : Set P) := by
   rintro _ ⟨i, j, hi, hj, rfl⟩; exact apply_mem_map₂ _ hi hj
 #align submodule.image2_subset_map₂ Submodule.image2_subset_map₂
+-/
 
+#print Submodule.map₂_eq_span_image2 /-
 theorem map₂_eq_span_image2 (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f p q = span R (Set.image2 (fun m n => f m n) (p : Set M) (q : Set N)) := by
   rw [← map₂_span_span, span_eq, span_eq]
 #align submodule.map₂_eq_span_image2 Submodule.map₂_eq_span_image2
+-/
 
+#print Submodule.map₂_flip /-
 theorem map₂_flip (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f.flip q p = map₂ f p q := by
   rw [map₂_eq_span_image2, map₂_eq_span_image2, Set.image2_swap]; rfl
 #align submodule.map₂_flip Submodule.map₂_flip
+-/
 
+#print Submodule.map₂_iSup_left /-
 theorem map₂_iSup_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule R M) (t : Submodule R N) :
     map₂ f (⨆ i, s i) t = ⨆ i, map₂ f (s i) t :=
   by
@@ -163,7 +190,9 @@ theorem map₂_iSup_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule R
     simpa only [span_eq] using this
   simp_rw [map₂_span_span, ← span_Union, map₂_span_span, Set.image2_iUnion_left]
 #align submodule.map₂_supr_left Submodule.map₂_iSup_left
+-/
 
+#print Submodule.map₂_iSup_right /-
 theorem map₂_iSup_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t : ι → Submodule R N) :
     map₂ f s (⨆ i, t i) = ⨆ i, map₂ f s (t i) :=
   by
@@ -171,7 +200,9 @@ theorem map₂_iSup_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t
     simpa only [span_eq] using this
   simp_rw [map₂_span_span, ← span_Union, map₂_span_span, Set.image2_iUnion_right]
 #align submodule.map₂_supr_right Submodule.map₂_iSup_right
+-/
 
+#print Submodule.map₂_span_singleton_eq_map /-
 theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
     map₂ f (span R {m}) = map (f m) := by
   funext; rw [map₂_eq_span_image2]; apply le_antisymm
@@ -183,10 +214,13 @@ theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
   · rintro _ ⟨n, hn, rfl⟩
     exact subset_span ⟨m, n, mem_span_singleton_self m, hn, rfl⟩
 #align submodule.map₂_span_singleton_eq_map Submodule.map₂_span_singleton_eq_map
+-/
 
+#print Submodule.map₂_span_singleton_eq_map_flip /-
 theorem map₂_span_singleton_eq_map_flip (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (n : N) :
     map₂ f s (span R {n}) = map (f.flip n) s := by rw [← map₂_span_singleton_eq_map, map₂_flip]
 #align submodule.map₂_span_singleton_eq_map_flip Submodule.map₂_span_singleton_eq_map_flip
+-/
 
 end Submodule

ee05e9ce

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -76,8 +76,8 @@ theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N)
   · rw [map₂_le]; intro a ha b hb
     apply span_induction ha
     on_goal 1 =>
-      intros ; apply span_induction hb
-      on_goal 1 => intros ; exact subset_span ⟨_, _, ‹_›, ‹_›, rfl⟩
+      intros; apply span_induction hb
+      on_goal 1 => intros; exact subset_span ⟨_, _, ‹_›, ‹_›, rfl⟩
     all_goals
       intros
       simp only [LinearMap.map_zero, LinearMap.zero_apply, zero_mem, LinearMap.map_add,
@@ -96,13 +96,13 @@ variable {R}
 @[simp]
 theorem map₂_bot_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) : map₂ f p ⊥ = ⊥ :=
   eq_bot_iff.2 <|
-    map₂_le.2 fun m hm n hn => by rw [Submodule.mem_bot] at hn⊢; rw [hn, LinearMap.map_zero]
+    map₂_le.2 fun m hm n hn => by rw [Submodule.mem_bot] at hn ⊢; rw [hn, LinearMap.map_zero]
 #align submodule.map₂_bot_right Submodule.map₂_bot_right
 
 @[simp]
 theorem map₂_bot_left (f : M →ₗ[R] N →ₗ[R] P) (q : Submodule R N) : map₂ f ⊥ q = ⊥ :=
   eq_bot_iff.2 <|
-    map₂_le.2 fun m hm n hn => by rw [Submodule.mem_bot] at hm⊢; rw [hm, LinearMap.map_zero₂]
+    map₂_le.2 fun m hm n hn => by rw [Submodule.mem_bot] at hm ⊢; rw [hm, LinearMap.map_zero₂]
 #align submodule.map₂_bot_left Submodule.map₂_bot_left
 
 @[mono]

ee05e9ce

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -35,9 +35,9 @@ universe uι u v
 
 open Set
 
-open BigOperators
+open scoped BigOperators
 
-open Pointwise
+open scoped Pointwise
 
 namespace Submodule

ee05e9ce

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -56,17 +56,11 @@ def map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R
 #align submodule.map₂ Submodule.map₂
 -/
 
-/- warning: submodule.apply_mem_map₂ -> Submodule.apply_mem_map₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_map₂ Submodule.apply_mem_map₂ₓ'. -/
 theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Submodule R M}
     {q : Submodule R N} (hm : m ∈ p) (hn : n ∈ q) : f m n ∈ map₂ f p q :=
   (le_iSup _ ⟨m, hm⟩ : _ ≤ map₂ f p q) ⟨n, hn, rfl⟩
 #align submodule.apply_mem_map₂ Submodule.apply_mem_map₂
 
-/- warning: submodule.map₂_le -> Submodule.map₂_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_le Submodule.map₂_leₓ'. -/
 theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submodule R N}
     {r : Submodule R P} : map₂ f p q ≤ r ↔ ∀ m ∈ p, ∀ n ∈ q, f m n ∈ r :=
   ⟨fun H m hm n hn => H <| apply_mem_map₂ _ hm hn, fun H =>
@@ -75,9 +69,6 @@ theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submo
 
 variable (R)
 
-/- warning: submodule.map₂_span_span -> Submodule.map₂_span_span is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_span Submodule.map₂_span_spanₓ'. -/
 theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N) :
     map₂ f (span R s) (span R t) = span R (Set.image2 (fun m n => f m n) s t) :=
   by
@@ -102,58 +93,34 @@ theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N)
 
 variable {R}
 
-/- warning: submodule.map₂_bot_right -> Submodule.map₂_bot_right is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p (Bot.bot.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Submodule.hasBot.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))) (Bot.bot.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.hasBot.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align submodule.map₂_bot_right Submodule.map₂_bot_rightₓ'. -/
 @[simp]
 theorem map₂_bot_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) : map₂ f p ⊥ = ⊥ :=
   eq_bot_iff.2 <|
     map₂_le.2 fun m hm n hn => by rw [Submodule.mem_bot] at hn⊢; rw [hn, LinearMap.map_zero]
 #align submodule.map₂_bot_right Submodule.map₂_bot_right
 
-/- warning: submodule.map₂_bot_left -> Submodule.map₂_bot_left is a dubious translation:
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-  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Bot.bot.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Submodule.hasBot.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)) q) (Bot.bot.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.hasBot.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))
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-Case conversion may be inaccurate. Consider using '#align submodule.map₂_bot_left Submodule.map₂_bot_leftₓ'. -/
 @[simp]
 theorem map₂_bot_left (f : M →ₗ[R] N →ₗ[R] P) (q : Submodule R N) : map₂ f ⊥ q = ⊥ :=
   eq_bot_iff.2 <|
     map₂_le.2 fun m hm n hn => by rw [Submodule.mem_bot] at hm⊢; rw [hm, LinearMap.map_zero₂]
 #align submodule.map₂_bot_left Submodule.map₂_bot_left
 
-/- warning: submodule.map₂_le_map₂ -> Submodule.map₂_le_map₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂ Submodule.map₂_le_map₂ₓ'. -/
 @[mono]
 theorem map₂_le_map₂ {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submodule R M} {q₁ q₂ : Submodule R N}
     (hp : p₁ ≤ p₂) (hq : q₁ ≤ q₂) : map₂ f p₁ q₁ ≤ map₂ f p₂ q₂ :=
   map₂_le.2 fun m hm n hn => apply_mem_map₂ _ (hp hm) (hq hn)
 #align submodule.map₂_le_map₂ Submodule.map₂_le_map₂
 
-/- warning: submodule.map₂_le_map₂_left -> Submodule.map₂_le_map₂_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂_left Submodule.map₂_le_map₂_leftₓ'. -/
 theorem map₂_le_map₂_left {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submodule R M} {q : Submodule R N}
     (h : p₁ ≤ p₂) : map₂ f p₁ q ≤ map₂ f p₂ q :=
   map₂_le_map₂ h (le_refl q)
 #align submodule.map₂_le_map₂_left Submodule.map₂_le_map₂_left
 
-/- warning: submodule.map₂_le_map₂_right -> Submodule.map₂_le_map₂_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂_right Submodule.map₂_le_map₂_rightₓ'. -/
 theorem map₂_le_map₂_right {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q₁ q₂ : Submodule R N}
     (h : q₁ ≤ q₂) : map₂ f p q₁ ≤ map₂ f p q₂ :=
   map₂_le_map₂ (le_refl p) h
 #align submodule.map₂_le_map₂_right Submodule.map₂_le_map₂_right
 
-/- warning: submodule.map₂_sup_right -> Submodule.map₂_sup_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_sup_right Submodule.map₂_sup_rightₓ'. -/
 theorem map₂_sup_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q₁ q₂ : Submodule R N) :
     map₂ f p (q₁ ⊔ q₂) = map₂ f p q₁ ⊔ map₂ f p q₂ :=
   le_antisymm
@@ -163,9 +130,6 @@ theorem map₂_sup_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q
     (sup_le (map₂_le_map₂_right le_sup_left) (map₂_le_map₂_right le_sup_right))
 #align submodule.map₂_sup_right Submodule.map₂_sup_right
 
-/- warning: submodule.map₂_sup_left -> Submodule.map₂_sup_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_sup_left Submodule.map₂_sup_leftₓ'. -/
 theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R M) (q : Submodule R N) :
     map₂ f (p₁ ⊔ p₂) q = map₂ f p₁ q ⊔ map₂ f p₂ q :=
   le_antisymm
@@ -177,33 +141,21 @@ theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R
     (sup_le (map₂_le_map₂_left le_sup_left) (map₂_le_map₂_left le_sup_right))
 #align submodule.map₂_sup_left Submodule.map₂_sup_left
 
-/- warning: submodule.image2_subset_map₂ -> Submodule.image2_subset_map₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.image2_subset_map₂ Submodule.image2_subset_map₂ₓ'. -/
 theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     Set.image2 (fun m n => f m n) (↑p : Set M) (↑q : Set N) ⊆ (↑(map₂ f p q) : Set P) := by
   rintro _ ⟨i, j, hi, hj, rfl⟩; exact apply_mem_map₂ _ hi hj
 #align submodule.image2_subset_map₂ Submodule.image2_subset_map₂
 
-/- warning: submodule.map₂_eq_span_image2 -> Submodule.map₂_eq_span_image2 is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_eq_span_image2 Submodule.map₂_eq_span_image2ₓ'. -/
 theorem map₂_eq_span_image2 (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f p q = span R (Set.image2 (fun m n => f m n) (p : Set M) (q : Set N)) := by
   rw [← map₂_span_span, span_eq, span_eq]
 #align submodule.map₂_eq_span_image2 Submodule.map₂_eq_span_image2
 
-/- warning: submodule.map₂_flip -> Submodule.map₂_flip is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_flip Submodule.map₂_flipₓ'. -/
 theorem map₂_flip (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f.flip q p = map₂ f p q := by
   rw [map₂_eq_span_image2, map₂_eq_span_image2, Set.image2_swap]; rfl
 #align submodule.map₂_flip Submodule.map₂_flip
 
-/- warning: submodule.map₂_supr_left -> Submodule.map₂_iSup_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_supr_left Submodule.map₂_iSup_leftₓ'. -/
 theorem map₂_iSup_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule R M) (t : Submodule R N) :
     map₂ f (⨆ i, s i) t = ⨆ i, map₂ f (s i) t :=
   by
@@ -212,9 +164,6 @@ theorem map₂_iSup_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule R
   simp_rw [map₂_span_span, ← span_Union, map₂_span_span, Set.image2_iUnion_left]
 #align submodule.map₂_supr_left Submodule.map₂_iSup_left
 
-/- warning: submodule.map₂_supr_right -> Submodule.map₂_iSup_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_supr_right Submodule.map₂_iSup_rightₓ'. -/
 theorem map₂_iSup_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t : ι → Submodule R N) :
     map₂ f s (⨆ i, t i) = ⨆ i, map₂ f s (t i) :=
   by
@@ -223,9 +172,6 @@ theorem map₂_iSup_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t
   simp_rw [map₂_span_span, ← span_Union, map₂_span_span, Set.image2_iUnion_right]
 #align submodule.map₂_supr_right Submodule.map₂_iSup_right
 
-/- warning: submodule.map₂_span_singleton_eq_map -> Submodule.map₂_span_singleton_eq_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map Submodule.map₂_span_singleton_eq_mapₓ'. -/
 theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
     map₂ f (span R {m}) = map (f m) := by
   funext; rw [map₂_eq_span_image2]; apply le_antisymm
@@ -238,9 +184,6 @@ theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
     exact subset_span ⟨m, n, mem_span_singleton_self m, hn, rfl⟩
 #align submodule.map₂_span_singleton_eq_map Submodule.map₂_span_singleton_eq_map
 
-/- warning: submodule.map₂_span_singleton_eq_map_flip -> Submodule.map₂_span_singleton_eq_map_flip is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map_flip Submodule.map₂_span_singleton_eq_map_flipₓ'. -/
 theorem map₂_span_singleton_eq_map_flip (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (n : N) :
     map₂ f s (span R {n}) = map (f.flip n) s := by rw [← map₂_span_singleton_eq_map, map₂_flip]
 #align submodule.map₂_span_singleton_eq_map_flip Submodule.map₂_span_singleton_eq_map_flip

ee05e9ce

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -82,8 +82,7 @@ theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N)
     map₂ f (span R s) (span R t) = span R (Set.image2 (fun m n => f m n) s t) :=
   by
   apply le_antisymm
-  · rw [map₂_le]
-    intro a ha b hb
+  · rw [map₂_le]; intro a ha b hb
     apply span_induction ha
     on_goal 1 =>
       intros ; apply span_induction hb
@@ -97,8 +96,7 @@ theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N)
         { max_depth := 4
           discharger := tactic.interactive.apply_instance }) [add_mem _ _, zero_mem _,
         smul_mem _ _ _]
-  · rw [span_le]
-    rintro _ ⟨a, b, ha, hb, rfl⟩
+  · rw [span_le]; rintro _ ⟨a, b, ha, hb, rfl⟩
     exact apply_mem_map₂ _ (subset_span ha) (subset_span hb)
 #align submodule.map₂_span_span Submodule.map₂_span_span
 
@@ -113,9 +111,7 @@ Case conversion may be inaccurate. Consider using '#align submodule.map₂_bot_r
 @[simp]
 theorem map₂_bot_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) : map₂ f p ⊥ = ⊥ :=
   eq_bot_iff.2 <|
-    map₂_le.2 fun m hm n hn => by
-      rw [Submodule.mem_bot] at hn⊢
-      rw [hn, LinearMap.map_zero]
+    map₂_le.2 fun m hm n hn => by rw [Submodule.mem_bot] at hn⊢; rw [hn, LinearMap.map_zero]
 #align submodule.map₂_bot_right Submodule.map₂_bot_right
 
 /- warning: submodule.map₂_bot_left -> Submodule.map₂_bot_left is a dubious translation:
@@ -127,9 +123,7 @@ Case conversion may be inaccurate. Consider using '#align submodule.map₂_bot_l
 @[simp]
 theorem map₂_bot_left (f : M →ₗ[R] N →ₗ[R] P) (q : Submodule R N) : map₂ f ⊥ q = ⊥ :=
   eq_bot_iff.2 <|
-    map₂_le.2 fun m hm n hn => by
-      rw [Submodule.mem_bot] at hm⊢
-      rw [hm, LinearMap.map_zero₂]
+    map₂_le.2 fun m hm n hn => by rw [Submodule.mem_bot] at hm⊢; rw [hm, LinearMap.map_zero₂]
 #align submodule.map₂_bot_left Submodule.map₂_bot_left
 
 /- warning: submodule.map₂_le_map₂ -> Submodule.map₂_le_map₂ is a dubious translation:
@@ -187,10 +181,8 @@ theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R
 <too large>
 Case conversion may be inaccurate. Consider using '#align submodule.image2_subset_map₂ Submodule.image2_subset_map₂ₓ'. -/
 theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
-    Set.image2 (fun m n => f m n) (↑p : Set M) (↑q : Set N) ⊆ (↑(map₂ f p q) : Set P) :=
-  by
-  rintro _ ⟨i, j, hi, hj, rfl⟩
-  exact apply_mem_map₂ _ hi hj
+    Set.image2 (fun m n => f m n) (↑p : Set M) (↑q : Set N) ⊆ (↑(map₂ f p q) : Set P) := by
+  rintro _ ⟨i, j, hi, hj, rfl⟩; exact apply_mem_map₂ _ hi hj
 #align submodule.image2_subset_map₂ Submodule.image2_subset_map₂
 
 /- warning: submodule.map₂_eq_span_image2 -> Submodule.map₂_eq_span_image2 is a dubious translation:
@@ -205,10 +197,8 @@ theorem map₂_eq_span_image2 (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M
 <too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_flip Submodule.map₂_flipₓ'. -/
 theorem map₂_flip (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
-    map₂ f.flip q p = map₂ f p q :=
-  by
-  rw [map₂_eq_span_image2, map₂_eq_span_image2, Set.image2_swap]
-  rfl
+    map₂ f.flip q p = map₂ f p q := by
+  rw [map₂_eq_span_image2, map₂_eq_span_image2, Set.image2_swap]; rfl
 #align submodule.map₂_flip Submodule.map₂_flip
 
 /- warning: submodule.map₂_supr_left -> Submodule.map₂_iSup_left is a dubious translation:

ee05e9ce

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -57,10 +57,7 @@ def map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_map₂ Submodule.apply_mem_map₂ₓ'. -/
 theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Submodule R M}
     {q : Submodule R N} (hm : m ∈ p) (hn : n ∈ q) : f m n ∈ map₂ f p q :=
@@ -68,10 +65,7 @@ theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Su
 #align submodule.apply_mem_map₂ Submodule.apply_mem_map₂
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le Submodule.map₂_leₓ'. -/
 theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submodule R N}
     {r : Submodule R P} : map₂ f p q ≤ r ↔ ∀ m ∈ p, ∀ n ∈ q, f m n ∈ r :=
@@ -82,10 +76,7 @@ theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submo
 variable (R)
 
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 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_span Submodule.map₂_span_spanₓ'. -/
 theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N) :
     map₂ f (span R s) (span R t) = span R (Set.image2 (fun m n => f m n) s t) :=
@@ -142,10 +133,7 @@ theorem map₂_bot_left (f : M →ₗ[R] N →ₗ[R] P) (q : Submodule R N) : ma
 #align submodule.map₂_bot_left Submodule.map₂_bot_left
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂ Submodule.map₂_le_map₂ₓ'. -/
 @[mono]
 theorem map₂_le_map₂ {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submodule R M} {q₁ q₂ : Submodule R N}
@@ -154,10 +142,7 @@ theorem map₂_le_map₂ {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submodule
 #align submodule.map₂_le_map₂ Submodule.map₂_le_map₂
 
 /- warning: submodule.map₂_le_map₂_left -> Submodule.map₂_le_map₂_left is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂_left Submodule.map₂_le_map₂_leftₓ'. -/
 theorem map₂_le_map₂_left {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submodule R M} {q : Submodule R N}
     (h : p₁ ≤ p₂) : map₂ f p₁ q ≤ map₂ f p₂ q :=
@@ -165,10 +150,7 @@ theorem map₂_le_map₂_left {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submo
 #align submodule.map₂_le_map₂_left Submodule.map₂_le_map₂_left
 
 /- warning: submodule.map₂_le_map₂_right -> Submodule.map₂_le_map₂_right is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂_right Submodule.map₂_le_map₂_rightₓ'. -/
 theorem map₂_le_map₂_right {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q₁ q₂ : Submodule R N}
     (h : q₁ ≤ q₂) : map₂ f p q₁ ≤ map₂ f p q₂ :=
@@ -176,10 +158,7 @@ theorem map₂_le_map₂_right {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R
 #align submodule.map₂_le_map₂_right Submodule.map₂_le_map₂_right
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_sup_right Submodule.map₂_sup_rightₓ'. -/
 theorem map₂_sup_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q₁ q₂ : Submodule R N) :
     map₂ f p (q₁ ⊔ q₂) = map₂ f p q₁ ⊔ map₂ f p q₂ :=
@@ -191,10 +170,7 @@ theorem map₂_sup_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q
 #align submodule.map₂_sup_right Submodule.map₂_sup_right
 
 /- warning: submodule.map₂_sup_left -> Submodule.map₂_sup_left is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_sup_left Submodule.map₂_sup_leftₓ'. -/
 theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R M) (q : Submodule R N) :
     map₂ f (p₁ ⊔ p₂) q = map₂ f p₁ q ⊔ map₂ f p₂ q :=
@@ -208,10 +184,7 @@ theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R
 #align submodule.map₂_sup_left Submodule.map₂_sup_left
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.image2_subset_map₂ Submodule.image2_subset_map₂ₓ'. -/
 theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     Set.image2 (fun m n => f m n) (↑p : Set M) (↑q : Set N) ⊆ (↑(map₂ f p q) : Set P) :=
@@ -221,10 +194,7 @@ theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M)
 #align submodule.image2_subset_map₂ Submodule.image2_subset_map₂
 
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 Case conversion may be inaccurate. Consider using '#align submodule.map₂_eq_span_image2 Submodule.map₂_eq_span_image2ₓ'. -/
 theorem map₂_eq_span_image2 (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f p q = span R (Set.image2 (fun m n => f m n) (p : Set M) (q : Set N)) := by
@@ -232,10 +202,7 @@ theorem map₂_eq_span_image2 (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M
 #align submodule.map₂_eq_span_image2 Submodule.map₂_eq_span_image2
 
 /- warning: submodule.map₂_flip -> Submodule.map₂_flip is a dubious translation:
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-  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u3, u2, u4} R N M P _inst_1 _inst_3 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f) q p) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q)
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-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u1, u3, u2} R N M P _inst_1 _inst_3 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (LinearMap.flip.{u4, u4, u4, u4, u3, u1, u2} R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) f) q p) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_flip Submodule.map₂_flipₓ'. -/
 theorem map₂_flip (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f.flip q p = map₂ f p q :=
@@ -245,10 +212,7 @@ theorem map₂_flip (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Sub
 #align submodule.map₂_flip Submodule.map₂_flip
 
 /- warning: submodule.map₂_supr_left -> Submodule.map₂_iSup_left is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_supr_left Submodule.map₂_iSup_leftₓ'. -/
 theorem map₂_iSup_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule R M) (t : Submodule R N) :
     map₂ f (⨆ i, s i) t = ⨆ i, map₂ f (s i) t :=
@@ -259,10 +223,7 @@ theorem map₂_iSup_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule R
 #align submodule.map₂_supr_left Submodule.map₂_iSup_left
 
 /- warning: submodule.map₂_supr_right -> Submodule.map₂_iSup_right is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_supr_right Submodule.map₂_iSup_rightₓ'. -/
 theorem map₂_iSup_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t : ι → Submodule R N) :
     map₂ f s (⨆ i, t i) = ⨆ i, map₂ f s (t i) :=
@@ -273,10 +234,7 @@ theorem map₂_iSup_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t
 #align submodule.map₂_supr_right Submodule.map₂_iSup_right
 
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 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map Submodule.map₂_span_singleton_eq_mapₓ'. -/
 theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
     map₂ f (span R {m}) = map (f m) := by
@@ -291,10 +249,7 @@ theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
 #align submodule.map₂_span_singleton_eq_map Submodule.map₂_span_singleton_eq_map
 
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(CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) 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R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) f) n) s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map_flip Submodule.map₂_span_singleton_eq_map_flipₓ'. -/
 theorem map₂_span_singleton_eq_map_flip (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (n : N) :
     map₂ f s (span R {n}) = map (f.flip n) s := by rw [← map₂_span_singleton_eq_map, map₂_flip]

ee05e9ce

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -60,7 +60,7 @@ def map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P 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 but is expected to have type
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(CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P 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+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) {m : M} {n : N} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R 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 Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_map₂ Submodule.apply_mem_map₂ₓ'. -/
 theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Submodule R M}
     {q : Submodule R N} (hm : m ∈ p) (hn : n ∈ q) : f m n ∈ map₂ f p q :=
@@ -71,7 +71,7 @@ theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Su
 lean 3 declaration is
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u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) r)))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {r : Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7}, Iff (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) r) (forall (m : M), (Membership.mem.{u3, u3} M (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) m p) -> (forall (n : N), (Membership.mem.{u1, u1} N (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) n) (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) r)))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {r : Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7}, Iff (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) r) (forall (m : M), (Membership.mem.{u3, u3} M (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) m p) -> (forall (n : N), (Membership.mem.{u1, u1} N (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) n) (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) 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(CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) r)))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le Submodule.map₂_leₓ'. -/
 theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submodule R N}
     {r : Submodule R P} : map₂ f p q ≤ r ↔ ∀ m ∈ p, ∀ n ∈ q, f m n ∈ r :=
@@ -85,7 +85,7 @@ variable (R)
 lean 3 declaration is
   forall (R : Type.{u1}) {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u2} M) (t : Set.{u3} N), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5 s) (Submodule.span.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6 t)) (Submodule.span.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7 (Set.image2.{u2, u3, u4} M N P (fun (m : M) (n : N) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) s t))
 but is expected to have type
-  forall (R : Type.{u4}) {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u3} M) (t : Set.{u1} N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5 s) (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 t)) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) s t))
+  forall (R : Type.{u4}) {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u3} M) (t : Set.{u1} N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5 s) (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 t)) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) s t))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_span Submodule.map₂_span_spanₓ'. -/
 theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N) :
     map₂ f (span R s) (span R t) = span R (Set.image2 (fun m n => f m n) s t) :=
@@ -211,7 +211,7 @@ theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), HasSubset.Subset.{u4} (Set.{u4} P) (Set.hasSubset.{u4} P) (Set.image2.{u2, u3, u4} M N P (fun (m : M) (n : N) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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_inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q)) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Set.{u4} P) (HasLiftT.mk.{succ u4, succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Set.{u4} P) (CoeTCₓ.coe.{succ u4, succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Set.{u4} P) (SetLike.Set.hasCoeT.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), HasSubset.Subset.{u2} (Set.{u2} P) (Set.instHasSubsetSet.{u2} P) (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} 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_inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)) (SetLike.coe.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), HasSubset.Subset.{u2} (Set.{u2} P) (Set.instHasSubsetSet.{u2} P) (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R 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(CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)) (SetLike.coe.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
 Case conversion may be inaccurate. Consider using '#align submodule.image2_subset_map₂ Submodule.image2_subset_map₂ₓ'. -/
 theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     Set.image2 (fun m n => f m n) (↑p : Set M) (↑q : Set N) ⊆ (↑(map₂ f p q) : Set P) :=
@@ -224,7 +224,7 @@ theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M)
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) (Submodule.span.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7 (Set.image2.{u2, u3, u4} M N P (fun (m : M) (n : N) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q)))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_eq_span_image2 Submodule.map₂_eq_span_image2ₓ'. -/
 theorem map₂_eq_span_image2 (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f p q = span R (Set.image2 (fun m n => f m n) (p : Set M) (q : Set N)) := by
@@ -276,7 +276,7 @@ theorem map₂_iSup_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (m : M), Eq.{max (succ u3) (succ u4)} ((Submodule.{u1, u3} R 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(LinearMap.semilinearMapClass.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (m : M), Eq.{max (succ u1) (succ u2)} ((Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) -> (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5 (Singleton.singleton.{u3, u3} M (Set.{u3} M) (Set.instSingletonSet.{u3} M) m))) (Submodule.map.{u4, u4, u1, u2, max u1 u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) (LinearMap.semilinearMapClass.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (m : M), Eq.{max (succ u1) (succ u2)} ((Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) -> (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5 (Singleton.singleton.{u3, u3} M (Set.{u3} M) (Set.instSingletonSet.{u3} M) m))) (Submodule.map.{u4, u4, u1, u2, max u1 u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) (LinearMap.semilinearMapClass.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map Submodule.map₂_span_singleton_eq_mapₓ'. -/
 theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
     map₂ f (span R {m}) = map (f m) := by
@@ -294,7 +294,7 @@ theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (n : N), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (Submodule.span.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6 (Singleton.singleton.{u3, u3} N (Set.{u3} N) (Set.hasSingleton.{u3} N) n))) (Submodule.map.{u1, u1, u2, u4, max u2 u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u3) (succ (max u2 u4)), max (succ u3) (succ (max u2 u4))} (LinearMap.{u1, u1, u3, max u2 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _inst_3 (LinearMap.addCommMonoid.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (LinearMap.flip._proof_1.{u1, u1, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) P _inst_4 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _inst_3 (LinearMap.addCommMonoid.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (LinearMap.flip._proof_1.{u1, u1, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) P _inst_4 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))))) => N -> (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u4} R R N (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 (LinearMap.addCommMonoid.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (LinearMap.flip._proof_1.{u1, u1, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) P _inst_4 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f) n) s)
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (n : N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 (Singleton.singleton.{u1, u1} N (Set.{u1} N) (Set.instSingletonSet.{u1} N) n))) (Submodule.map.{u4, u4, u3, u2, max u3 u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) n) (LinearMap.semilinearMapClass.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u1, max (succ u3) (succ u2)} (LinearMap.{u4, u4, u1, max u2 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u2} R R N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.flip.{u4, u4, u4, u4, u3, u1, u2} R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) f) n) s)
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (n : N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 (Singleton.singleton.{u1, u1} N (Set.{u1} N) (Set.instSingletonSet.{u1} N) n))) (Submodule.map.{u4, u4, u3, u2, max u3 u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) n) (LinearMap.semilinearMapClass.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u1, max (succ u3) (succ u2)} (LinearMap.{u4, u4, u1, max u2 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u2} R R N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.flip.{u4, u4, u4, u4, u3, u1, u2} R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) f) n) s)
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map_flip Submodule.map₂_span_singleton_eq_map_flipₓ'. -/
 theorem map₂_span_singleton_eq_map_flip (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (n : N) :
     map₂ f s (span R {n}) = map (f.flip n) s := by rw [← map₂_span_singleton_eq_map, map₂_flip]

ee05e9ce

bump to nightly-2023-05-18-03

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

b46e9d53

Diff

@@ -60,7 +60,7 @@ def map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) {m : M} {n : N} {p : Submodule.{u1, u2} R M 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(Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 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(LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R 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 but is expected to have type
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(CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) {m : M} {n : N} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6}, (Membership.mem.{u3, u3} M (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) m p) -> (Membership.mem.{u1, u1} N (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) n) (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R P 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 Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_map₂ Submodule.apply_mem_map₂ₓ'. -/
 theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Submodule R M}
     {q : Submodule R N} (hm : m ∈ p) (hn : n ∈ q) : f m n ∈ map₂ f p q :=
@@ -71,7 +71,7 @@ theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Su
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P 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(CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R 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(LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) r)))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {r : Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7}, Iff (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) r) (forall (m : M), (Membership.mem.{u3, u3} M (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) m p) -> (forall (n : N), (Membership.mem.{u1, u1} N (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) n) (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) r)))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {r : Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7}, Iff (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) r) (forall (m : M), (Membership.mem.{u3, u3} M (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) m p) -> (forall (n : N), (Membership.mem.{u1, u1} N (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) n) (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) r)))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le Submodule.map₂_leₓ'. -/
 theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submodule R N}
     {r : Submodule R P} : map₂ f p q ≤ r ↔ ∀ m ∈ p, ∀ n ∈ q, f m n ∈ r :=
@@ -85,7 +85,7 @@ variable (R)
 lean 3 declaration is
   forall (R : Type.{u1}) {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u2} M) (t : Set.{u3} N), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5 s) (Submodule.span.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6 t)) (Submodule.span.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7 (Set.image2.{u2, u3, u4} M N P (fun (m : M) (n : N) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) s t))
 but is expected to have type
-  forall (R : Type.{u4}) {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u3} M) (t : Set.{u1} N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5 s) (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 t)) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) s t))
+  forall (R : Type.{u4}) {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u3} M) (t : Set.{u1} N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5 s) (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 t)) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) s t))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_span Submodule.map₂_span_spanₓ'. -/
 theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N) :
     map₂ f (span R s) (span R t) = span R (Set.image2 (fun m n => f m n) s t) :=
@@ -211,7 +211,7 @@ theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), HasSubset.Subset.{u4} (Set.{u4} P) (Set.hasSubset.{u4} P) (Set.image2.{u2, u3, u4} M N P (fun (m : M) (n : N) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R 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 but is expected to have type
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_inst_6 _inst_7 f p q))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), HasSubset.Subset.{u2} (Set.{u2} P) (Set.instHasSubsetSet.{u2} P) (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) 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_inst_6 _inst_7 f p q))
 Case conversion may be inaccurate. Consider using '#align submodule.image2_subset_map₂ Submodule.image2_subset_map₂ₓ'. -/
 theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     Set.image2 (fun m n => f m n) (↑p : Set M) (↑q : Set N) ⊆ (↑(map₂ f p q) : Set P) :=
@@ -224,7 +224,7 @@ theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M)
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P 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(MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q)))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) 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_inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_eq_span_image2 Submodule.map₂_eq_span_image2ₓ'. -/
 theorem map₂_eq_span_image2 (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f p q = span R (Set.image2 (fun m n => f m n) (p : Set M) (q : Set N)) := by
@@ -276,7 +276,7 @@ theorem map₂_iSup_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (m : M), Eq.{max (succ u3) (succ u4)} ((Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) -> (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) m))) (Submodule.map.{u1, u1, u3, u4, max u3 u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (m : M), Eq.{max (succ u1) (succ u2)} ((Submodule.{u4, u1} R N 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M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R 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+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P 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 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map Submodule.map₂_span_singleton_eq_mapₓ'. -/
 theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
     map₂ f (span R {m}) = map (f m) := by
@@ -294,7 +294,7 @@ theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (LinearMap.flip._proof_1.{u1, u1, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) P _inst_4 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))))) (fun (_x : 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_inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (LinearMap.flip._proof_1.{u1, u1, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) P _inst_4 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))))) => N -> (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u4} R R N (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 (LinearMap.addCommMonoid.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (LinearMap.flip._proof_1.{u1, u1, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) P _inst_4 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f) n) s)
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (n : N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 (Singleton.singleton.{u1, u1} N (Set.{u1} N) (Set.instSingletonSet.{u1} N) n))) (Submodule.map.{u4, u4, u3, u2, max u3 u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) n) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u1, max (succ u3) (succ u2)} (LinearMap.{u4, u4, u1, max u2 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u2} R R N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.flip.{u4, u4, u4, u4, u3, u1, u2} R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) f) n) s)
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (n : N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 (Singleton.singleton.{u1, u1} N (Set.{u1} N) (Set.instSingletonSet.{u1} N) n))) (Submodule.map.{u4, u4, u3, u2, max u3 u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) n) (LinearMap.semilinearMapClass.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u1, max (succ u3) (succ u2)} (LinearMap.{u4, u4, u1, max u2 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R 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R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) f) n) s)
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map_flip Submodule.map₂_span_singleton_eq_map_flipₓ'. -/
 theorem map₂_span_singleton_eq_map_flip (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (n : N) :
     map₂ f s (span R {n}) = map (f.flip n) s := by rw [← map₂_span_singleton_eq_map, map₂_flip]

ee05e9ce

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -69,7 +69,7 @@ theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Su
 
 /- warning: submodule.map₂_le -> Submodule.map₂_le is a dubious translation:
 lean 3 declaration is
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(LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) r)))
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R 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(LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) r)))
 but is expected to have type
   forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {r : Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7}, Iff (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) r) (forall (m : M), (Membership.mem.{u3, u3} M (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) m p) -> (forall (n : N), (Membership.mem.{u1, u1} N (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) n) (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) r)))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le Submodule.map₂_leₓ'. -/
@@ -143,7 +143,7 @@ theorem map₂_bot_left (f : M →ₗ[R] N →ₗ[R] P) (q : Submodule R N) : ma
 
 /- warning: submodule.map₂_le_map₂ -> Submodule.map₂_le_map₂ is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p₁ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {p₂ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q₁ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6} {q₂ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6}, (LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p₁ p₂) -> (LE.le.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Preorder.toLE.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q₁ q₂) -> (LE.le.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q₁) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q₂))
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p₁ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {p₂ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q₁ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6} {q₂ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6}, (LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p₁ p₂) -> (LE.le.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q₁ q₂) -> (LE.le.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Preorder.toHasLe.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q₁) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q₂))
 but is expected to have type
   forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p₁ : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {p₂ : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q₁ : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {q₂ : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6}, (LE.le.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Preorder.toLE.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (PartialOrder.toPreorder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5))))) p₁ p₂) -> (LE.le.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Preorder.toLE.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Submodule.completeLattice.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6))))) q₁ q₂) -> (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q₁) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q₂))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂ Submodule.map₂_le_map₂ₓ'. -/
@@ -155,7 +155,7 @@ theorem map₂_le_map₂ {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submodule
 
 /- warning: submodule.map₂_le_map₂_left -> Submodule.map₂_le_map₂_left is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p₁ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {p₂ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6}, (LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p₁ p₂) -> (LE.le.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q))
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p₁ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {p₂ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6}, (LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p₁ p₂) -> (LE.le.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Preorder.toHasLe.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q))
 but is expected to have type
   forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p₁ : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {p₂ : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6}, (LE.le.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Preorder.toLE.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (PartialOrder.toPreorder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5))))) p₁ p₂) -> (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂_left Submodule.map₂_le_map₂_leftₓ'. -/
@@ -166,7 +166,7 @@ theorem map₂_le_map₂_left {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submo
 
 /- warning: submodule.map₂_le_map₂_right -> Submodule.map₂_le_map₂_right is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q₁ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6} {q₂ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6}, (LE.le.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Preorder.toLE.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q₁ q₂) -> (LE.le.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₁) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₂))
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q₁ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6} {q₂ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6}, (LE.le.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q₁ q₂) -> (LE.le.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Preorder.toHasLe.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₁) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₂))
 but is expected to have type
   forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q₁ : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {q₂ : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6}, (LE.le.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Preorder.toLE.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Submodule.completeLattice.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6))))) q₁ q₂) -> (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₁) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₂))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂_right Submodule.map₂_le_map₂_rightₓ'. -/

ee05e9ce

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -64,7 +64,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_map₂ Submodule.apply_mem_map₂ₓ'. -/
 theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Submodule R M}
     {q : Submodule R N} (hm : m ∈ p) (hn : n ∈ q) : f m n ∈ map₂ f p q :=
-  (le_supᵢ _ ⟨m, hm⟩ : _ ≤ map₂ f p q) ⟨n, hn, rfl⟩
+  (le_iSup _ ⟨m, hm⟩ : _ ≤ map₂ f p q) ⟨n, hn, rfl⟩
 #align submodule.apply_mem_map₂ Submodule.apply_mem_map₂
 
 /- warning: submodule.map₂_le -> Submodule.map₂_le is a dubious translation:
@@ -76,7 +76,7 @@ Case conversion may be inaccurate. Consider using '#align submodule.map₂_le Su
 theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submodule R N}
     {r : Submodule R P} : map₂ f p q ≤ r ↔ ∀ m ∈ p, ∀ n ∈ q, f m n ∈ r :=
   ⟨fun H m hm n hn => H <| apply_mem_map₂ _ hm hn, fun H =>
-    supᵢ_le fun ⟨m, hm⟩ => map_le_iff_le_comap.2 fun n hn => H m hm n hn⟩
+    iSup_le fun ⟨m, hm⟩ => map_le_iff_le_comap.2 fun n hn => H m hm n hn⟩
 #align submodule.map₂_le Submodule.map₂_le
 
 variable (R)
@@ -244,33 +244,33 @@ theorem map₂_flip (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Sub
   rfl
 #align submodule.map₂_flip Submodule.map₂_flip
 
-/- warning: submodule.map₂_supr_left -> Submodule.map₂_supᵢ_left is a dubious translation:
+/- warning: submodule.map₂_supr_left -> Submodule.map₂_iSup_left is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} N] [_inst_4 : AddCommMonoid.{u5} P] [_inst_5 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_6 : Module.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3] [_inst_7 : Module.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] (f : LinearMap.{u2, u2, u3, max u4 u5} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M (LinearMap.{u2, u2, u4, u5} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u4, u5} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (LinearMap.module.{u2, u2, u2, u4, u5} R R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7 (smulCommClass_self.{u2, u5} R P (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u5} R P (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_4))) (Module.toMulActionWithZero.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7))))) (s : ι -> (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5)) (t : Submodule.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6), Eq.{succ u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u2, u3, u4, u5} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (supᵢ.{u3, u1} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5))) ι (fun (i : ι) => s i)) t) (supᵢ.{u5, u1} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toHasSup.{u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7))) ι (fun (i : ι) => Submodule.map₂.{u2, u3, u4, u5} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i) t))
+  forall {ι : Sort.{u1}} {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} N] [_inst_4 : AddCommMonoid.{u5} P] [_inst_5 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_6 : Module.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3] [_inst_7 : Module.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] (f : LinearMap.{u2, u2, u3, max u4 u5} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M (LinearMap.{u2, u2, u4, u5} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u4, u5} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (LinearMap.module.{u2, u2, u2, u4, u5} R R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7 (smulCommClass_self.{u2, u5} R P (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u5} R P (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_4))) (Module.toMulActionWithZero.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7))))) (s : ι -> (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5)) (t : Submodule.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6), Eq.{succ u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u2, u3, u4, u5} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (iSup.{u3, u1} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5))) ι (fun (i : ι) => s i)) t) (iSup.{u5, u1} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toHasSup.{u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7))) ι (fun (i : ι) => Submodule.map₂.{u2, u3, u4, u5} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i) t))
 but is expected to have type
-  forall {ι : Sort.{u5}} {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : ι -> (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) (t : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (supᵢ.{u3, u5} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5))) ι (fun (i : ι) => s i)) t) (supᵢ.{u2, u5} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) ι (fun (i : ι) => Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i) t))
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_supr_left Submodule.map₂_supᵢ_leftₓ'. -/
-theorem map₂_supᵢ_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule R M) (t : Submodule R N) :
+  forall {ι : Sort.{u5}} {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : ι -> (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) (t : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (iSup.{u3, u5} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5))) ι (fun (i : ι) => s i)) t) (iSup.{u2, u5} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) ι (fun (i : ι) => Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i) t))
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_supr_left Submodule.map₂_iSup_leftₓ'. -/
+theorem map₂_iSup_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule R M) (t : Submodule R N) :
     map₂ f (⨆ i, s i) t = ⨆ i, map₂ f (s i) t :=
   by
   suffices map₂ f (⨆ i, span R (s i : Set M)) (span R t) = ⨆ i, map₂ f (span R (s i)) (span R t) by
     simpa only [span_eq] using this
-  simp_rw [map₂_span_span, ← span_Union, map₂_span_span, Set.image2_unionᵢ_left]
-#align submodule.map₂_supr_left Submodule.map₂_supᵢ_left
+  simp_rw [map₂_span_span, ← span_Union, map₂_span_span, Set.image2_iUnion_left]
+#align submodule.map₂_supr_left Submodule.map₂_iSup_left
 
-/- warning: submodule.map₂_supr_right -> Submodule.map₂_supᵢ_right is a dubious translation:
+/- warning: submodule.map₂_supr_right -> Submodule.map₂_iSup_right is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} N] [_inst_4 : AddCommMonoid.{u5} P] [_inst_5 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_6 : Module.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3] [_inst_7 : Module.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] (f : LinearMap.{u2, u2, u3, max u4 u5} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M (LinearMap.{u2, u2, u4, u5} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u4, u5} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (LinearMap.module.{u2, u2, u2, u4, u5} R R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7 (smulCommClass_self.{u2, u5} R P (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u5} R P (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_4))) (Module.toMulActionWithZero.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5) (t : ι -> (Submodule.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6)), Eq.{succ u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u2, u3, u4, u5} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (supᵢ.{u4, u1} (Submodule.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6) (ConditionallyCompleteLattice.toHasSup.{u4} (Submodule.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u4} (Submodule.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6) (Submodule.completeLattice.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6))) ι (fun (i : ι) => t i))) (supᵢ.{u5, u1} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toHasSup.{u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7))) ι (fun (i : ι) => Submodule.map₂.{u2, u3, u4, u5} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (t i)))
+  forall {ι : Sort.{u1}} {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} N] [_inst_4 : AddCommMonoid.{u5} P] [_inst_5 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_6 : Module.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3] [_inst_7 : Module.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] (f : LinearMap.{u2, u2, u3, max u4 u5} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M (LinearMap.{u2, u2, u4, u5} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u4, u5} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (LinearMap.module.{u2, u2, u2, u4, u5} R R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7 (smulCommClass_self.{u2, u5} R P (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u5} R P (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_4))) (Module.toMulActionWithZero.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5) (t : ι -> (Submodule.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6)), Eq.{succ u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u2, u3, u4, u5} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (iSup.{u4, u1} (Submodule.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6) (ConditionallyCompleteLattice.toHasSup.{u4} (Submodule.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u4} (Submodule.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6) (Submodule.completeLattice.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6))) ι (fun (i : ι) => t i))) (iSup.{u5, u1} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toHasSup.{u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7))) ι (fun (i : ι) => Submodule.map₂.{u2, u3, u4, u5} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (t i)))
 but is expected to have type
-  forall {ι : Sort.{u5}} {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (t : ι -> (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (supᵢ.{u1, u5} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Submodule.completeLattice.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6))) ι (fun (i : ι) => t i))) (supᵢ.{u2, u5} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) ι (fun (i : ι) => Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (t i)))
-Case conversion may be inaccurate. Consider using '#align submodule.map₂_supr_right Submodule.map₂_supᵢ_rightₓ'. -/
-theorem map₂_supᵢ_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t : ι → Submodule R N) :
+  forall {ι : Sort.{u5}} {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (t : ι -> (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (iSup.{u1, u5} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Submodule.completeLattice.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6))) ι (fun (i : ι) => t i))) (iSup.{u2, u5} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) ι (fun (i : ι) => Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (t i)))
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_supr_right Submodule.map₂_iSup_rightₓ'. -/
+theorem map₂_iSup_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t : ι → Submodule R N) :
     map₂ f s (⨆ i, t i) = ⨆ i, map₂ f s (t i) :=
   by
   suffices map₂ f (span R s) (⨆ i, span R (t i : Set N)) = ⨆ i, map₂ f (span R s) (span R (t i)) by
     simpa only [span_eq] using this
-  simp_rw [map₂_span_span, ← span_Union, map₂_span_span, Set.image2_unionᵢ_right]
-#align submodule.map₂_supr_right Submodule.map₂_supᵢ_right
+  simp_rw [map₂_span_span, ← span_Union, map₂_span_span, Set.image2_iUnion_right]
+#align submodule.map₂_supr_right Submodule.map₂_iSup_right
 
 /- warning: submodule.map₂_span_singleton_eq_map -> Submodule.map₂_span_singleton_eq_map is a dubious translation:
 lean 3 declaration is

ee05e9ce

bump to nightly-2023-03-18-14

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

73d15350

Diff

@@ -60,7 +60,7 @@ def map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) {m : M} {n : N} {p : Submodule.{u1, u2} R M 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 but is expected to have type
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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) {m : M} {n : N} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6}, (Membership.mem.{u3, u3} M (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) m p) -> (Membership.mem.{u1, u1} N (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) n) (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R P 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(AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
 Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_map₂ Submodule.apply_mem_map₂ₓ'. -/
 theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Submodule R M}
     {q : Submodule R N} (hm : m ∈ p) (hn : n ∈ q) : f m n ∈ map₂ f p q :=
@@ -71,7 +71,7 @@ theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Su
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6} {r : Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7}, Iff (LE.le.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) r) (forall (m : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M 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(CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R 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(LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) r)))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {r : Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7}, Iff (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) r) (forall (m : M), (Membership.mem.{u3, u3} M (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) m p) -> (forall (n : N), (Membership.mem.{u1, u1} N (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.instSetLikeSubmodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) n) (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.instSetLikeSubmodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R 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_inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) r)))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {r : Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7}, Iff (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) r) (forall (m : M), (Membership.mem.{u3, u3} M (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) m p) -> (forall (n : N), (Membership.mem.{u1, u1} N (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) n) (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) r)))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le Submodule.map₂_leₓ'. -/
 theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submodule R N}
     {r : Submodule R P} : map₂ f p q ≤ r ↔ ∀ m ∈ p, ∀ n ∈ q, f m n ∈ r :=
@@ -211,7 +211,7 @@ theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), HasSubset.Subset.{u4} (Set.{u4} P) (Set.hasSubset.{u4} P) (Set.image2.{u2, u3, u4} M N P (fun (m : M) (n : N) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q)) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Set.{u4} P) (HasLiftT.mk.{succ u4, succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Set.{u4} P) (CoeTCₓ.coe.{succ u4, succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Set.{u4} P) (SetLike.Set.hasCoeT.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), HasSubset.Subset.{u2} (Set.{u2} P) (Set.instHasSubsetSet.{u2} P) (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.instSetLikeSubmodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)) (SetLike.coe.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.instSetLikeSubmodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), HasSubset.Subset.{u2} (Set.{u2} P) (Set.instHasSubsetSet.{u2} P) (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)) (SetLike.coe.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
 Case conversion may be inaccurate. Consider using '#align submodule.image2_subset_map₂ Submodule.image2_subset_map₂ₓ'. -/
 theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     Set.image2 (fun m n => f m n) (↑p : Set M) (↑q : Set N) ⊆ (↑(map₂ f p q) : Set P) :=
@@ -224,7 +224,7 @@ theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M)
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) (Submodule.span.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7 (Set.image2.{u2, u3, u4} M N P (fun (m : M) (n : N) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q)))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) 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_inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.instSetLikeSubmodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_eq_span_image2 Submodule.map₂_eq_span_image2ₓ'. -/
 theorem map₂_eq_span_image2 (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f p q = span R (Set.image2 (fun m n => f m n) (p : Set M) (q : Set N)) := by

ee05e9ce

bump to nightly-2023-03-11-22

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

a8ee822f

Diff

@@ -60,7 +60,7 @@ def map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) {m : M} {n : N} {p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)) m p) -> (Membership.Mem.{u3, u3} N (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.Mem.{u4, u4} P (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.hasMem.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 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(LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R 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 but is expected to have type
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(CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) {m : M} {n : N} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6}, (Membership.mem.{u3, u3} M (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) m p) -> (Membership.mem.{u1, u1} N (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.instSetLikeSubmodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) n) (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SetLike.instMembership.{u2, u2} 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+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P 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(CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
 Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_map₂ Submodule.apply_mem_map₂ₓ'. -/
 theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Submodule R M}
     {q : Submodule R N} (hm : m ∈ p) (hn : n ∈ q) : f m n ∈ map₂ f p q :=
@@ -71,7 +71,7 @@ theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Su
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6} {r : Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7}, Iff (LE.le.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) r) (forall (m : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)) m p) -> (forall (n : N), (Membership.Mem.{u3, u3} N (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.Mem.{u4, u4} P (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.hasMem.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R 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(LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) r)))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {r : Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7}, Iff (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) r) (forall (m : M), (Membership.mem.{u3, u3} M (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) m p) -> (forall (n : N), (Membership.mem.{u1, u1} N (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.instSetLikeSubmodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)) n q) -> (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) n) (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P 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(Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) r)))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {r : Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7}, Iff (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) r) (forall (m : M), 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(Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) r)))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_le Submodule.map₂_leₓ'. -/
 theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submodule R N}
     {r : Submodule R P} : map₂ f p q ≤ r ↔ ∀ m ∈ p, ∀ n ∈ q, f m n ∈ r :=
@@ -85,7 +85,7 @@ variable (R)
 lean 3 declaration is
   forall (R : Type.{u1}) {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u2} M) (t : Set.{u3} N), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5 s) (Submodule.span.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6 t)) (Submodule.span.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7 (Set.image2.{u2, u3, u4} M N P (fun (m : M) (n : N) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) s t))
 but is expected to have type
-  forall (R : Type.{u4}) {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u3} M) (t : Set.{u1} N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5 s) (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 t)) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) s t))
+  forall (R : Type.{u4}) {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u3} M) (t : Set.{u1} N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5 s) (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 t)) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) s t))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_span Submodule.map₂_span_spanₓ'. -/
 theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N) :
     map₂ f (span R s) (span R t) = span R (Set.image2 (fun m n => f m n) s t) :=
@@ -211,7 +211,7 @@ theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), HasSubset.Subset.{u4} (Set.{u4} P) (Set.hasSubset.{u4} P) (Set.image2.{u2, u3, u4} M N P (fun (m : M) (n : N) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R 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_inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q)) ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Set.{u4} P) (HasLiftT.mk.{succ u4, succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Set.{u4} P) (CoeTCₓ.coe.{succ u4, succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Set.{u4} P) (SetLike.Set.hasCoeT.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), HasSubset.Subset.{u2} (Set.{u2} P) (Set.instHasSubsetSet.{u2} P) (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} 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_inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.instSetLikeSubmodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)) (SetLike.coe.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.instSetLikeSubmodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), HasSubset.Subset.{u2} (Set.{u2} P) (Set.instHasSubsetSet.{u2} P) (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) 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(CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.instSetLikeSubmodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)) (SetLike.coe.{u2, u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) P (Submodule.instSetLikeSubmodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q))
 Case conversion may be inaccurate. Consider using '#align submodule.image2_subset_map₂ Submodule.image2_subset_map₂ₓ'. -/
 theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     Set.image2 (fun m n => f m n) (↑p : Set M) (↑q : Set N) ⊆ (↑(map₂ f p q) : Set P) :=
@@ -224,7 +224,7 @@ theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M)
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) (Submodule.span.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7 (Set.image2.{u2, u3, u4} M N P (fun (m : M) (n : N) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Set.{u3} N) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q)))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.instSetLikeSubmodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) (SetLike.coe.{u3, u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) M (Submodule.instSetLikeSubmodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) p) (SetLike.coe.{u1, u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) N (Submodule.instSetLikeSubmodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) q)))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_eq_span_image2 Submodule.map₂_eq_span_image2ₓ'. -/
 theorem map₂_eq_span_image2 (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f p q = span R (Set.image2 (fun m n => f m n) (p : Set M) (q : Set N)) := by
@@ -276,7 +276,7 @@ theorem map₂_supᵢ_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M)
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (m : M), Eq.{max (succ u3) (succ u4)} ((Submodule.{u1, u3} R 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(LinearMap.semilinearMapClass.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (m : M), Eq.{max (succ u1) (succ u2)} ((Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) -> (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5 (Singleton.singleton.{u3, u3} M (Set.{u3} M) (Set.instSingletonSet.{u3} M) m))) (Submodule.map.{u4, u4, u1, u2, max u1 u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m))
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (m : M), Eq.{max (succ u1) (succ u2)} ((Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) -> (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5 (Singleton.singleton.{u3, u3} M (Set.{u3} M) (Set.instSingletonSet.{u3} M) m))) (Submodule.map.{u4, u4, u1, u2, max u1 u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map Submodule.map₂_span_singleton_eq_mapₓ'. -/
 theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
     map₂ f (span R {m}) = map (f m) := by
@@ -294,7 +294,7 @@ theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (n : N), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (Submodule.span.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6 (Singleton.singleton.{u3, u3} N (Set.{u3} N) (Set.hasSingleton.{u3} N) n))) (Submodule.map.{u1, u1, u2, u4, max u2 u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u3) (succ (max u2 u4)), max (succ u3) (succ (max u2 u4))} (LinearMap.{u1, u1, u3, max u2 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _inst_3 (LinearMap.addCommMonoid.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (LinearMap.flip._proof_1.{u1, u1, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) P _inst_4 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _inst_3 (LinearMap.addCommMonoid.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (LinearMap.flip._proof_1.{u1, u1, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) P _inst_4 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))))) => N -> (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u4} R R N (LinearMap.{u1, u1, u2, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 (LinearMap.addCommMonoid.{u1, u1, u2, u4} R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_6 (LinearMap.module.{u1, u1, u1, u2, u4} R R R M P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (LinearMap.flip._proof_1.{u1, u1, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) P _inst_4 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f) n) s)
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (n : N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 (Singleton.singleton.{u1, u1} N (Set.{u1} N) (Set.instSingletonSet.{u1} N) n))) (Submodule.map.{u4, u4, u3, u2, max u3 u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) n) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u1, max (succ u3) (succ u2)} (LinearMap.{u4, u4, u1, max u2 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u2} R R N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.flip.{u4, u4, u4, u4, u3, u1, u2} R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) f) n) s)
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (n : N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 (Singleton.singleton.{u1, u1} N (Set.{u1} N) (Set.instSingletonSet.{u1} N) n))) (Submodule.map.{u4, u4, u3, u2, max u3 u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) n) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u1, max (succ u3) (succ u2)} (LinearMap.{u4, u4, u1, max u2 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u2} R R N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.flip.{u4, u4, u4, u4, u3, u1, u2} R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) f) n) s)
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map_flip Submodule.map₂_span_singleton_eq_map_flipₓ'. -/
 theorem map₂_span_singleton_eq_map_flip (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (n : N) :
     map₂ f s (span R {n}) = map (f.flip n) s := by rw [← map₂_span_singleton_eq_map, map₂_flip]

ee05e9ce

bump to nightly-2023-03-04-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

51aaf796

Diff

@@ -85,7 +85,7 @@ variable (R)
 lean 3 declaration is
   forall (R : Type.{u1}) {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u2} M) (t : Set.{u3} N), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5 s) (Submodule.span.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6 t)) (Submodule.span.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7 (Set.image2.{u2, u3, u4} M N P (fun (m : M) (n : N) => coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (fun (_x : LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (coeFn.{max (succ u2) (succ (max u3 u4)), max (succ u2) (succ (max u3 u4))} (LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) => M -> (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7)) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u4} R R M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) f m) n) s t))
 but is expected to have type
-  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u3} M) (t : Set.{u1} N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Submodule.span.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5 s) (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 t)) (Submodule.span.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7 (Set.image2.{u3, u1, u2} M N P (fun (m : M) (n : N) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) m) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u1 u2} R R M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) s t))
+  forall (R : Type.{u4}) {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Set.{u3} M) (t : Set.{u1} N), Eq.{succ u2} (Submodule.{u4, u2} R P 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) f m) n) s t))
 Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_span Submodule.map₂_span_spanₓ'. -/
 theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N) :
     map₂ f (span R s) (span R t) = span R (Set.image2 (fun m n => f m n) s t) :=

ee05e9ce

bump to nightly-2023-03-02-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

db7421c3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Eric Wieser
 
 ! This file was ported from Lean 3 source module algebra.module.submodule.bilinear
-! leanprover-community/mathlib commit 6010cf523816335f7bae7f8584cb2edaace73940
+! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
 ! 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.BilinearMap
 /-!
 # Images of pairs of submodules under bilinear maps
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file provides `submodule.map₂`, which is later used to implement `submodule.has_mul`.
 
 ## Main results

6010cf52

bump to nightly-2023-02-28-12

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

208d1f40

Diff

@@ -44,18 +44,32 @@ variable [CommSemiring R] [AddCommMonoid M] [AddCommMonoid N] [AddCommMonoid P]
 
 variable [Module R M] [Module R N] [Module R P]
 
+#print Submodule.map₂ /-
 /-- Map a pair of submodules under a bilinear map.
 
 This is the submodule version of `set.image2`.  -/
 def map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) : Submodule R P :=
   ⨆ s : p, q.map <| f s
 #align submodule.map₂ Submodule.map₂
+-/
 
+/- warning: submodule.apply_mem_map₂ -> Submodule.apply_mem_map₂ 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.apply_mem_map₂ Submodule.apply_mem_map₂ₓ'. -/
 theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Submodule R M}
     {q : Submodule R N} (hm : m ∈ p) (hn : n ∈ q) : f m n ∈ map₂ f p q :=
   (le_supᵢ _ ⟨m, hm⟩ : _ ≤ map₂ f p q) ⟨n, hn, rfl⟩
 #align submodule.apply_mem_map₂ Submodule.apply_mem_map₂
 
+/- warning: submodule.map₂_le -> Submodule.map₂_le 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.map₂_le Submodule.map₂_leₓ'. -/
 theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submodule R N}
     {r : Submodule R P} : map₂ f p q ≤ r ↔ ∀ m ∈ p, ∀ n ∈ q, f m n ∈ r :=
   ⟨fun H m hm n hn => H <| apply_mem_map₂ _ hm hn, fun H =>
@@ -64,6 +78,12 @@ theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submo
 
 variable (R)
 
+/- warning: submodule.map₂_span_span -> Submodule.map₂_span_span is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P 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+Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_span Submodule.map₂_span_spanₓ'. -/
 theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N) :
     map₂ f (span R s) (span R t) = span R (Set.image2 (fun m n => f m n) s t) :=
   by
@@ -90,6 +110,12 @@ theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N)
 
 variable {R}
 
+/- warning: submodule.map₂_bot_right -> Submodule.map₂_bot_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p (Bot.bot.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Submodule.hasBot.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))) (Bot.bot.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.hasBot.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))
+but is expected to have type
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p (Bot.bot.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Submodule.instBotSubmodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6))) (Bot.bot.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.instBotSubmodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_bot_right Submodule.map₂_bot_rightₓ'. -/
 @[simp]
 theorem map₂_bot_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) : map₂ f p ⊥ = ⊥ :=
   eq_bot_iff.2 <|
@@ -98,6 +124,12 @@ theorem map₂_bot_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) : m
       rw [hn, LinearMap.map_zero]
 #align submodule.map₂_bot_right Submodule.map₂_bot_right
 
+/- warning: submodule.map₂_bot_left -> Submodule.map₂_bot_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Bot.bot.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Submodule.hasBot.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)) q) (Bot.bot.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.hasBot.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))
+but is expected to have type
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Bot.bot.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Submodule.instBotSubmodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) q) (Bot.bot.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.instBotSubmodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_bot_left Submodule.map₂_bot_leftₓ'. -/
 @[simp]
 theorem map₂_bot_left (f : M →ₗ[R] N →ₗ[R] P) (q : Submodule R N) : map₂ f ⊥ q = ⊥ :=
   eq_bot_iff.2 <|
@@ -106,22 +138,46 @@ theorem map₂_bot_left (f : M →ₗ[R] N →ₗ[R] P) (q : Submodule R N) : ma
       rw [hm, LinearMap.map_zero₂]
 #align submodule.map₂_bot_left Submodule.map₂_bot_left
 
+/- warning: submodule.map₂_le_map₂ -> Submodule.map₂_le_map₂ is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p₁ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {p₂ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q₁ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6} {q₂ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6}, (LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p₁ p₂) -> (LE.le.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Preorder.toLE.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q₁ q₂) -> (LE.le.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q₁) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q₂))
+but is expected to have type
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p₁ : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {p₂ : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q₁ : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {q₂ : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6}, (LE.le.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Preorder.toLE.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (PartialOrder.toPreorder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5))))) p₁ p₂) -> (LE.le.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Preorder.toLE.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Submodule.completeLattice.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6))))) q₁ q₂) -> (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q₁) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q₂))
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂ Submodule.map₂_le_map₂ₓ'. -/
 @[mono]
 theorem map₂_le_map₂ {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submodule R M} {q₁ q₂ : Submodule R N}
     (hp : p₁ ≤ p₂) (hq : q₁ ≤ q₂) : map₂ f p₁ q₁ ≤ map₂ f p₂ q₂ :=
   map₂_le.2 fun m hm n hn => apply_mem_map₂ _ (hp hm) (hq hn)
 #align submodule.map₂_le_map₂ Submodule.map₂_le_map₂
 
+/- warning: submodule.map₂_le_map₂_left -> Submodule.map₂_le_map₂_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p₁ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {p₂ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6}, (LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) M (Submodule.setLike.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5)))) p₁ p₂) -> (LE.le.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q))
+but is expected to have type
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p₁ : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {p₂ : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6}, (LE.le.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Preorder.toLE.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (PartialOrder.toPreorder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5))))) p₁ p₂) -> (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q))
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂_left Submodule.map₂_le_map₂_leftₓ'. -/
 theorem map₂_le_map₂_left {f : M →ₗ[R] N →ₗ[R] P} {p₁ p₂ : Submodule R M} {q : Submodule R N}
     (h : p₁ ≤ p₂) : map₂ f p₁ q ≤ map₂ f p₂ q :=
   map₂_le_map₂ h (le_refl q)
 #align submodule.map₂_le_map₂_left Submodule.map₂_le_map₂_left
 
+/- warning: submodule.map₂_le_map₂_right -> Submodule.map₂_le_map₂_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5} {q₁ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6} {q₂ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6}, (LE.le.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Preorder.toLE.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) N (Submodule.setLike.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) q₁ q₂) -> (LE.le.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SetLike.partialOrder.{u4, u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) P (Submodule.setLike.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7)))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₁) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₂))
+but is expected to have type
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] {f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))} {p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5} {q₁ : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6} {q₂ : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6}, (LE.le.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Preorder.toLE.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Submodule.completeLattice.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6))))) q₁ q₂) -> (LE.le.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Preorder.toLE.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₁) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₂))
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_le_map₂_right Submodule.map₂_le_map₂_rightₓ'. -/
 theorem map₂_le_map₂_right {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q₁ q₂ : Submodule R N}
     (h : q₁ ≤ q₂) : map₂ f p q₁ ≤ map₂ f p q₂ :=
   map₂_le_map₂ (le_refl p) h
 #align submodule.map₂_le_map₂_right Submodule.map₂_le_map₂_right
 
+/- warning: submodule.map₂_sup_right -> Submodule.map₂_sup_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (q₁ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (q₂ : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p (Sup.sup.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Submodule.completeLattice.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))) q₁ q₂)) (Sup.sup.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SemilatticeSup.toHasSup.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Lattice.toSemilatticeSup.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toLattice.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₁) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₂))
+but is expected to have type
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q₁ : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (q₂ : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p (Sup.sup.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (SemilatticeSup.toSup.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Lattice.toSemilatticeSup.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Submodule.completeLattice.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6))))) q₁ q₂)) (Sup.sup.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SemilatticeSup.toSup.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Lattice.toSemilatticeSup.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₁) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q₂))
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_sup_right Submodule.map₂_sup_rightₓ'. -/
 theorem map₂_sup_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q₁ q₂ : Submodule R N) :
     map₂ f p (q₁ ⊔ q₂) = map₂ f p q₁ ⊔ map₂ f p q₂ :=
   le_antisymm
@@ -131,6 +187,12 @@ theorem map₂_sup_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q
     (sup_le (map₂_le_map₂_right le_sup_left) (map₂_le_map₂_right le_sup_right))
 #align submodule.map₂_sup_right Submodule.map₂_sup_right
 
+/- warning: submodule.map₂_sup_left -> Submodule.map₂_sup_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p₁ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (p₂ : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5))))) p₁ p₂) q) (Sup.sup.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (SemilatticeSup.toHasSup.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Lattice.toSemilatticeSup.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toLattice.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q))
+but is expected to have type
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p₁ : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (p₂ : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Sup.sup.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (SemilatticeSup.toSup.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Lattice.toSemilatticeSup.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5))))) p₁ p₂) q) (Sup.sup.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (SemilatticeSup.toSup.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Lattice.toSemilatticeSup.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₁ q) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p₂ q))
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_sup_left Submodule.map₂_sup_leftₓ'. -/
 theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R M) (q : Submodule R N) :
     map₂ f (p₁ ⊔ p₂) q = map₂ f p₁ q ⊔ map₂ f p₂ q :=
   le_antisymm
@@ -142,6 +204,12 @@ theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R
     (sup_le (map₂_le_map₂_left le_sup_left) (map₂_le_map₂_left le_sup_right))
 #align submodule.map₂_sup_left Submodule.map₂_sup_left
 
+/- warning: submodule.image2_subset_map₂ -> Submodule.image2_subset_map₂ 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.image2_subset_map₂ Submodule.image2_subset_map₂ₓ'. -/
 theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     Set.image2 (fun m n => f m n) (↑p : Set M) (↑q : Set N) ⊆ (↑(map₂ f p q) : Set P) :=
   by
@@ -149,11 +217,23 @@ theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M)
   exact apply_mem_map₂ _ hi hj
 #align submodule.image2_subset_map₂ Submodule.image2_subset_map₂
 
+/- warning: submodule.map₂_eq_span_image2 -> Submodule.map₂_eq_span_image2 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.map₂_eq_span_image2 Submodule.map₂_eq_span_image2ₓ'. -/
 theorem map₂_eq_span_image2 (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f p q = span R (Set.image2 (fun m n => f m n) (p : Set M) (q : Set N)) := by
   rw [← map₂_span_span, span_eq, span_eq]
 #align submodule.map₂_eq_span_image2 Submodule.map₂_eq_span_image2
 
+/- warning: submodule.map₂_flip -> Submodule.map₂_flip is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {P : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : AddCommMonoid.{u4} P] [_inst_5 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : Module.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] (f : LinearMap.{u1, u1, u2, max u3 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) M (LinearMap.{u1, u1, u3, u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u4} R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_5 (LinearMap.module.{u1, u1, u1, u3, u4} R R R N P (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u1, u3} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u1, u3, u2, u4} R N M P _inst_1 _inst_3 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u4} R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u1, u4} R P (CommSemiring.toCommMonoid.{u1} R _inst_1) (MulActionWithZero.toMulAction.{u1, u4} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f) q p) (Submodule.map₂.{u1, u2, u3, u4} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q)
+but is expected to have type
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (p : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (q : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u1, u3, u2} R N M P _inst_1 _inst_3 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (LinearMap.flip.{u4, u4, u4, u4, u3, u1, u2} R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) f) q p) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f p q)
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_flip Submodule.map₂_flipₓ'. -/
 theorem map₂_flip (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     map₂ f.flip q p = map₂ f p q :=
   by
@@ -161,6 +241,12 @@ theorem map₂_flip (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Sub
   rfl
 #align submodule.map₂_flip Submodule.map₂_flip
 
+/- warning: submodule.map₂_supr_left -> Submodule.map₂_supᵢ_left is a dubious translation:
+lean 3 declaration is
+  forall {ι : Sort.{u1}} {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u4}} {P : Type.{u5}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u4} N] [_inst_4 : AddCommMonoid.{u5} P] [_inst_5 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_6 : Module.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3] [_inst_7 : Module.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4] (f : LinearMap.{u2, u2, u3, max u4 u5} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M (LinearMap.{u2, u2, u4, u5} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u4, u5} R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_5 (LinearMap.module.{u2, u2, u2, u4, u5} R R R N P (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7 (smulCommClass_self.{u2, u5} R P (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u5} R P (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u5} P (AddMonoid.toAddZeroClass.{u5} P (AddCommMonoid.toAddMonoid.{u5} P _inst_4))) (Module.toMulActionWithZero.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7))))) (s : ι -> (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5)) (t : Submodule.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 _inst_6), Eq.{succ u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u2, u3, u4, u5} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (supᵢ.{u3, u1} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_5))) ι (fun (i : ι) => s i)) t) (supᵢ.{u5, u1} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toHasSup.{u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u5} (Submodule.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u2, u5} R P (CommSemiring.toSemiring.{u2} R _inst_1) _inst_4 _inst_7))) ι (fun (i : ι) => Submodule.map₂.{u2, u3, u4, u5} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i) t))
+but is expected to have type
+  forall {ι : Sort.{u5}} {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : ι -> (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5)) (t : Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (supᵢ.{u3, u5} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (Submodule.completeLattice.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5))) ι (fun (i : ι) => s i)) t) (supᵢ.{u2, u5} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) ι (fun (i : ι) => Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i) t))
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_supr_left Submodule.map₂_supᵢ_leftₓ'. -/
 theorem map₂_supᵢ_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule R M) (t : Submodule R N) :
     map₂ f (⨆ i, s i) t = ⨆ i, map₂ f (s i) t :=
   by
@@ -169,6 +255,12 @@ theorem map₂_supᵢ_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule
   simp_rw [map₂_span_span, ← span_Union, map₂_span_span, Set.image2_unionᵢ_left]
 #align submodule.map₂_supr_left Submodule.map₂_supᵢ_left
 
+/- warning: submodule.map₂_supr_right -> Submodule.map₂_supᵢ_right is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ι : Sort.{u5}} {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (t : ι -> (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6)), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (supᵢ.{u1, u5} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6) (Submodule.completeLattice.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6))) ι (fun (i : ι) => t i))) (supᵢ.{u2, u5} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.completeLattice.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) ι (fun (i : ι) => Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (t i)))
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_supr_right Submodule.map₂_supᵢ_rightₓ'. -/
 theorem map₂_supᵢ_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t : ι → Submodule R N) :
     map₂ f s (⨆ i, t i) = ⨆ i, map₂ f s (t i) :=
   by
@@ -177,6 +269,12 @@ theorem map₂_supᵢ_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M)
   simp_rw [map₂_span_span, ← span_Union, map₂_span_span, Set.image2_unionᵢ_right]
 #align submodule.map₂_supr_right Submodule.map₂_supᵢ_right
 
+/- warning: submodule.map₂_span_singleton_eq_map -> Submodule.map₂_span_singleton_eq_map is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map Submodule.map₂_span_singleton_eq_mapₓ'. -/
 theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
     map₂ f (span R {m}) = map (f m) := by
   funext; rw [map₂_eq_span_image2]; apply le_antisymm
@@ -189,6 +287,12 @@ theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
     exact subset_span ⟨m, n, mem_span_singleton_self m, hn, rfl⟩
 #align submodule.map₂_span_singleton_eq_map Submodule.map₂_span_singleton_eq_map
 
+/- warning: submodule.map₂_span_singleton_eq_map_flip -> Submodule.map₂_span_singleton_eq_map_flip is a dubious translation:
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(AddZeroClass.toHasZero.{u4} P (AddMonoid.toAddZeroClass.{u4} P (AddCommMonoid.toAddMonoid.{u4} P _inst_4))) (Module.toMulActionWithZero.{u1, u4} R P (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) f) n) s)
+but is expected to have type
+  forall {R : Type.{u4}} {M : Type.{u3}} {N : Type.{u1}} {P : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : AddCommMonoid.{u1} N] [_inst_4 : AddCommMonoid.{u2} P] [_inst_5 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_6 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_7 : Module.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4] (f : LinearMap.{u4, u4, u3, max u2 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N P _inst_3 _inst_4 _inst_6 _inst_7) _inst_2 (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_5 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R N P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_4 _inst_6 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (s : Submodule.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_5) (n : N), Eq.{succ u2} (Submodule.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7) (Submodule.map₂.{u4, u3, u1, u2} R M N P _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s (Submodule.span.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 _inst_6 (Singleton.singleton.{u1, u1} N (Set.{u1} N) (Set.instSingletonSet.{u1} N) n))) (Submodule.map.{u4, u4, u3, u2, max u3 u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomSurjective.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) n) (LinearMap.instSemilinearMapClassLinearMap.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u1, max (succ u3) (succ u2)} (LinearMap.{u4, u4, u1, max u2 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u1, max u3 u2} R R N (LinearMap.{u4, u4, u3, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M P _inst_2 _inst_4 _inst_5 _inst_7) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (LinearMap.addCommMonoid.{u4, u4, u3, u2} R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_6 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u2} R R R M P (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_4 _inst_5 _inst_7 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 (SMulCommClass.symm.{u2, u4, u4} R R P (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (SMulZeroClass.toSMul.{u4, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (SMulWithZero.toSMulZeroClass.{u4, u2} R P (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (MulActionWithZero.toSMulWithZero.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7)))) (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.flip.{u4, u4, u4, u4, u3, u1, u2} R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) R (CommSemiring.toSemiring.{u4} R _inst_1) M N P _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_7 (smulCommClass_self.{u4, u2} R P (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R P (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P _inst_4)) (Module.toMulActionWithZero.{u4, u2} R P (CommSemiring.toSemiring.{u4} R _inst_1) _inst_4 _inst_7))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) f) n) s)
+Case conversion may be inaccurate. Consider using '#align submodule.map₂_span_singleton_eq_map_flip Submodule.map₂_span_singleton_eq_map_flipₓ'. -/
 theorem map₂_span_singleton_eq_map_flip (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (n : N) :
     map₂ f s (span R {n}) = map (f.flip n) s := by rw [← map₂_span_singleton_eq_map, map₂_flip]
 #align submodule.map₂_span_singleton_eq_map_flip Submodule.map₂_span_singleton_eq_map_flip

6010cf52

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

6010cf52

refactor(LinearAlgebra): replace Submodule.restrictBilinear by BilinForm.restrict (#12045)

As discussed in this thread, there were 3 different definitions for the restriction of a bilinear form to a subspace. This PR deletes the definition Submodule.restrictBilinear, and replaces all its occurrences by the LinearMap.BilinForm.restrict one.

66924a04

Diff

@@ -168,17 +168,3 @@ theorem map₂_span_singleton_eq_map_flip (f : M →ₗ[R] N →ₗ[R] P) (s : S
 #align submodule.map₂_span_singleton_eq_map_flip Submodule.map₂_span_singleton_eq_map_flip
 
 end Submodule
-
-lemma LinearMap.ker_restrictBilinear_eq_of_codisjoint
-    {R M : Type*} [CommSemiring R] [AddCommMonoid M] [Module R M]
-    {p q : Submodule R M} (hpq : Codisjoint p q)
-    {B : LinearMap.BilinForm R M} (hB : ∀ x ∈ p, ∀ y ∈ q, B x y = 0) :
-    LinearMap.ker (p.restrictBilinear B) = (LinearMap.ker B).comap p.subtype := by
-  ext ⟨z, hz⟩
-  simp only [LinearMap.mem_ker, Submodule.mem_comap, Submodule.coeSubtype]
-  refine ⟨fun h ↦ ?_, fun h ↦ ?_⟩
-  · ext w
-    obtain ⟨x, hx, y, hy, rfl⟩ := Submodule.exists_add_eq_of_codisjoint hpq w
-    simpa [hB z hz y hy] using LinearMap.congr_fun h ⟨x, hx⟩
-  · ext ⟨x, hx⟩
-    simpa using LinearMap.congr_fun h x

6010cf52

chore: remove some unnecessary 'open BigOperators' (#11880)

Could we have an open linter, that checked for unused opened namespaces?

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

16eb4bdf

Diff

@@ -29,8 +29,6 @@ universe uι u v
 
 open Set
 
-open BigOperators
-
 open Pointwise
 
 namespace Submodule

6010cf52

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -36,9 +36,7 @@ open Pointwise
 namespace Submodule
 
 variable {ι : Sort uι} {R M N P : Type*}
-
 variable [CommSemiring R] [AddCommMonoid M] [AddCommMonoid N] [AddCommMonoid P]
-
 variable [Module R M] [Module R N] [Module R P]
 
 /-- Map a pair of submodules under a bilinear map.

6010cf52

chore(LinearAlgebra): Introduce a LinearMap.BilinForm alias (#10632)

This is one of the steps in #10553.

Once we eliminate _root_.BilinForm, we can drop the LinearMap. prefix.

Requested on Zulip by me (2021), [by @kmill](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/.60bilinear_form.60/near/310675731) (2022), and perhaps one or two other places.

Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com>

2ef6133e

Diff

@@ -176,7 +176,7 @@ end Submodule
 lemma LinearMap.ker_restrictBilinear_eq_of_codisjoint
     {R M : Type*} [CommSemiring R] [AddCommMonoid M] [Module R M]
     {p q : Submodule R M} (hpq : Codisjoint p q)
-    {B : M →ₗ[R] M →ₗ[R] R} (hB : ∀ x ∈ p, ∀ y ∈ q, B x y = 0) :
+    {B : LinearMap.BilinForm R M} (hB : ∀ x ∈ p, ∀ y ∈ q, B x y = 0) :
     LinearMap.ker (p.restrictBilinear B) = (LinearMap.ker B).comap p.subtype := by
   ext ⟨z, hz⟩
   simp only [LinearMap.mem_ker, Submodule.mem_comap, Submodule.coeSubtype]

6010cf52

refactor(*): change definition of Set.image2 etc (#9275)

Redefine Set.image2 to use ∃ a ∈ s, ∃ b ∈ t, f a b = c instead of ∃ a b, a ∈ s ∧ b ∈ t ∧ f a b = c.
Redefine Set.seq as Set.image2. The new definition is equal to the old one but rw [Set.seq] gives a different result.
Redefine Filter.map₂ to use ∃ u ∈ f, ∃ v ∈ g, image2 m u v ⊆ s instead of ∃ u v, u ∈ f ∧ v ∈ g ∧ ...
Update lemmas like Set.mem_image2, Finset.mem_image₂, Set.mem_mul, Finset.mem_div etc

The two reasons to make the change are:

∃ a ∈ s, ∃ b ∈ t, _ is a simp-normal form, and
it looks a bit nicer.

8f17470f

Diff

@@ -68,12 +68,12 @@ theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N)
     intro a ha
     apply @span_induction' R N _ _ _ t
     intro b hb
-    exact subset_span ⟨_, _, ‹_›, ‹_›, rfl⟩
+    exact subset_span ⟨_, ‹_›, _, ‹_›, rfl⟩
     all_goals intros; simp only [*, add_mem, smul_mem, zero_mem, _root_.map_zero, map_add,
                                  LinearMap.zero_apply, LinearMap.add_apply, LinearMap.smul_apply,
                                  map_smul]
-  · rw [span_le]
-    rintro _ ⟨a, b, ha, hb, rfl⟩
+  · rw [span_le, image2_subset_iff]
+    intro a ha b hb
     exact apply_mem_map₂ _ (subset_span ha) (subset_span hb)
 #align submodule.map₂_span_span Submodule.map₂_span_span
 variable {R}
@@ -132,7 +132,7 @@ theorem map₂_sup_left (f : M →ₗ[R] N →ₗ[R] P) (p₁ p₂ : Submodule R
 
 theorem image2_subset_map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) :
     Set.image2 (fun m n => f m n) (↑p : Set M) (↑q : Set N) ⊆ (↑(map₂ f p q) : Set P) := by
-  rintro _ ⟨i, j, hi, hj, rfl⟩
+  rintro _ ⟨i, hi, j, hj, rfl⟩
   exact apply_mem_map₂ _ hi hj
 #align submodule.image2_subset_map₂ Submodule.image2_subset_map₂

6010cf52

chore(Submodule/Bilinear): golf a proof (#9057)

c371f598

Diff

@@ -163,14 +163,8 @@ theorem map₂_iSup_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t
 
 theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
     map₂ f (span R {m}) = map (f m) := by
-  funext; rw [map₂_eq_span_image2]; apply le_antisymm
-  · rw [span_le, Set.image2_subset_iff]
-    intro x hx y hy
-    obtain ⟨a, rfl⟩ := mem_span_singleton.1 hx
-    rw [f.map_smul]
-    exact smul_mem _ a (mem_map_of_mem hy)
-  · rintro _ ⟨n, hn, rfl⟩
-    exact subset_span ⟨m, n, mem_span_singleton_self m, hn, rfl⟩
+  funext s
+  rw [← span_eq s, map₂_span_span, image2_singleton_left, map_span]
 #align submodule.map₂_span_singleton_eq_map Submodule.map₂_span_singleton_eq_map
 
 theorem map₂_span_singleton_eq_map_flip (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (n : N) :

6010cf52

chore(Order/Filter): protect Filter.map_smul (#8935)

We use SMulHomClass.map_smul much more often, even when the Filter namespace is opened.

06295115

Diff

@@ -71,7 +71,7 @@ theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N)
     exact subset_span ⟨_, _, ‹_›, ‹_›, rfl⟩
     all_goals intros; simp only [*, add_mem, smul_mem, zero_mem, _root_.map_zero, map_add,
                                  LinearMap.zero_apply, LinearMap.add_apply, LinearMap.smul_apply,
-                                 SMulHomClass.map_smul]
+                                 map_smul]
   · rw [span_le]
     rintro _ ⟨a, b, ha, hb, rfl⟩
     exact apply_mem_map₂ _ (subset_span ha) (subset_span hb)

6010cf52

feat: a non-singular Killing form remains non-singular when restricted to a Cartan subalgebra (#7613)

They key addition is the lemma LieAlgebra.IsKilling.ker_restrictBilinear_of_isCartanSubalgebra_eq_bot.

11add7fe

Diff

@@ -178,3 +178,17 @@ theorem map₂_span_singleton_eq_map_flip (f : M →ₗ[R] N →ₗ[R] P) (s : S
 #align submodule.map₂_span_singleton_eq_map_flip Submodule.map₂_span_singleton_eq_map_flip
 
 end Submodule
+
+lemma LinearMap.ker_restrictBilinear_eq_of_codisjoint
+    {R M : Type*} [CommSemiring R] [AddCommMonoid M] [Module R M]
+    {p q : Submodule R M} (hpq : Codisjoint p q)
+    {B : M →ₗ[R] M →ₗ[R] R} (hB : ∀ x ∈ p, ∀ y ∈ q, B x y = 0) :
+    LinearMap.ker (p.restrictBilinear B) = (LinearMap.ker B).comap p.subtype := by
+  ext ⟨z, hz⟩
+  simp only [LinearMap.mem_ker, Submodule.mem_comap, Submodule.coeSubtype]
+  refine ⟨fun h ↦ ?_, fun h ↦ ?_⟩
+  · ext w
+    obtain ⟨x, hx, y, hy, rfl⟩ := Submodule.exists_add_eq_of_codisjoint hpq w
+    simpa [hB z hz y hy] using LinearMap.congr_fun h ⟨x, hx⟩
+  · ext ⟨x, hx⟩
+    simpa using LinearMap.congr_fun h x

6010cf52

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -35,7 +35,7 @@ open Pointwise
 
 namespace Submodule
 
-variable {ι : Sort uι} {R M N P : Type _}
+variable {ι : Sort uι} {R M N P : Type*}
 
 variable [CommSemiring R] [AddCommMonoid M] [AddCommMonoid N] [AddCommMonoid P]

6010cf52

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.module.submodule.bilinear
-! leanprover-community/mathlib commit 6010cf523816335f7bae7f8584cb2edaace73940
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Span
 import Mathlib.LinearAlgebra.BilinearMap
 
+#align_import algebra.module.submodule.bilinear from "leanprover-community/mathlib"@"6010cf523816335f7bae7f8584cb2edaace73940"
+
 /-!
 # Images of pairs of submodules under bilinear maps

6010cf52

fix: precedences of ⨆⋃⋂⨅ (#5614)

e3c8f983

Diff

@@ -48,7 +48,7 @@ variable [Module R M] [Module R N] [Module R P]
 
 This is the submodule version of `Set.image2`.  -/
 def map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R N) : Submodule R P :=
-  ⨆ s : p, q.map <| f s
+  ⨆ s : p, q.map (f s)
 #align submodule.map₂ Submodule.map₂
 
 theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Submodule R M}

6010cf52

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -93,7 +93,7 @@ theorem map₂_bot_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) : m
 theorem map₂_bot_left (f : M →ₗ[R] N →ₗ[R] P) (q : Submodule R N) : map₂ f ⊥ q = ⊥ :=
   eq_bot_iff.2 <|
     map₂_le.2 fun m hm n hn => by
-      rw [Submodule.mem_bot] at hm⊢
+      rw [Submodule.mem_bot] at hm ⊢
       rw [hm, LinearMap.map_zero₂]
 #align submodule.map₂_bot_left Submodule.map₂_bot_left

6010cf52

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

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

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

d1eb6264

Diff

@@ -53,13 +53,13 @@ def map₂ (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Submodule R
 
 theorem apply_mem_map₂ (f : M →ₗ[R] N →ₗ[R] P) {m : M} {n : N} {p : Submodule R M}
     {q : Submodule R N} (hm : m ∈ p) (hn : n ∈ q) : f m n ∈ map₂ f p q :=
-  (le_supᵢ _ ⟨m, hm⟩ : _ ≤ map₂ f p q) ⟨n, hn, by rfl⟩
+  (le_iSup _ ⟨m, hm⟩ : _ ≤ map₂ f p q) ⟨n, hn, by rfl⟩
 #align submodule.apply_mem_map₂ Submodule.apply_mem_map₂
 
 theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submodule R N}
     {r : Submodule R P} : map₂ f p q ≤ r ↔ ∀ m ∈ p, ∀ n ∈ q, f m n ∈ r :=
   ⟨fun H _m hm _n hn => H <| apply_mem_map₂ _ hm hn, fun H =>
-    supᵢ_le fun ⟨m, hm⟩ => map_le_iff_le_comap.2 fun n hn => H m hm n hn⟩
+    iSup_le fun ⟨m, hm⟩ => map_le_iff_le_comap.2 fun n hn => H m hm n hn⟩
 #align submodule.map₂_le Submodule.map₂_le
 
 variable (R)
@@ -150,19 +150,19 @@ theorem map₂_flip (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) (q : Sub
   rfl
 #align submodule.map₂_flip Submodule.map₂_flip
 
-theorem map₂_supᵢ_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule R M) (t : Submodule R N) :
+theorem map₂_iSup_left (f : M →ₗ[R] N →ₗ[R] P) (s : ι → Submodule R M) (t : Submodule R N) :
     map₂ f (⨆ i, s i) t = ⨆ i, map₂ f (s i) t := by
   suffices map₂ f (⨆ i, span R (s i : Set M)) (span R t) = ⨆ i, map₂ f (span R (s i)) (span R t) by
     simpa only [span_eq] using this
-  simp_rw [map₂_span_span, ← span_unionᵢ, map₂_span_span, Set.image2_unionᵢ_left]
-#align submodule.map₂_supr_left Submodule.map₂_supᵢ_left
+  simp_rw [map₂_span_span, ← span_iUnion, map₂_span_span, Set.image2_iUnion_left]
+#align submodule.map₂_supr_left Submodule.map₂_iSup_left
 
-theorem map₂_supᵢ_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t : ι → Submodule R N) :
+theorem map₂_iSup_right (f : M →ₗ[R] N →ₗ[R] P) (s : Submodule R M) (t : ι → Submodule R N) :
     map₂ f s (⨆ i, t i) = ⨆ i, map₂ f s (t i) := by
   suffices map₂ f (span R s) (⨆ i, span R (t i : Set N)) = ⨆ i, map₂ f (span R s) (span R (t i)) by
     simpa only [span_eq] using this
-  simp_rw [map₂_span_span, ← span_unionᵢ, map₂_span_span, Set.image2_unionᵢ_right]
-#align submodule.map₂_supr_right Submodule.map₂_supᵢ_right
+  simp_rw [map₂_span_span, ← span_iUnion, map₂_span_span, Set.image2_iUnion_right]
+#align submodule.map₂_supr_right Submodule.map₂_iSup_right
 
 theorem map₂_span_singleton_eq_map (f : M →ₗ[R] N →ₗ[R] P) (m : M) :
     map₂ f (span R {m}) = map (f m) := by

6010cf52

feat: port Algebra.Algebra.Operations (#2568)

This had some trouble with leanprover/lean4#2074 and leanprover/lean4#1926. There are also quite a few places where extra unfolding is needed in initializers for new-style structures.

Co-authored-by: Johan Commelin <johan@commelin.net>

7eadacc0

Diff

@@ -62,6 +62,7 @@ theorem map₂_le {f : M →ₗ[R] N →ₗ[R] P} {p : Submodule R M} {q : Submo
     supᵢ_le fun ⟨m, hm⟩ => map_le_iff_le_comap.2 fun n hn => H m hm n hn⟩
 #align submodule.map₂_le Submodule.map₂_le
 
+variable (R)
 theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N) :
     map₂ f (span R s) (span R t) = span R (Set.image2 (fun m n => f m n) s t) := by
   apply le_antisymm
@@ -78,6 +79,7 @@ theorem map₂_span_span (f : M →ₗ[R] N →ₗ[R] P) (s : Set M) (t : Set N)
     rintro _ ⟨a, b, ha, hb, rfl⟩
     exact apply_mem_map₂ _ (subset_span ha) (subset_span hb)
 #align submodule.map₂_span_span Submodule.map₂_span_span
+variable {R}
 
 @[simp]
 theorem map₂_bot_right (f : M →ₗ[R] N →ₗ[R] P) (p : Submodule R M) : map₂ f p ⊥ = ⊥ :=

6010cf52

feat: Port Algebra.Module.Submodule.Bilinear (#2531)

cd441518

`algebra.module.submodule.bilinear` ⟷ `Mathlib.Algebra.Module.Submodule.Bilinear`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 358

algebra.module.submodule.bilinear ⟷ Mathlib.Algebra.Module.Submodule.Bilinear

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 358

`algebra.module.submodule.bilinear` ⟷ `Mathlib.Algebra.Module.Submodule.Bilinear`