case mk.mk.mk.mk.mk.mk
R : Type u
L : Type v
M : Type w
N : Type w₁
P : Type w₂
inst✝¹⁴ : CommRing R
inst✝¹³ : LieRing L
inst✝¹² : LieAlgebra R L
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : AddCommGroup N
inst✝⁹ : AddCommGroup P
inst✝⁸ : Module R M
inst✝⁷ : Module R N
inst✝⁶ : Module R P
inst✝⁵ : LieRingModule L M
inst✝⁴ : LieRingModule L N
inst✝³ : LieRingModule L P
inst✝² : LieModule R L M
inst✝¹ : LieModule R L N
inst✝ : LieModule R L P
f : M → N
map_add'✝¹ : ∀ (x y : M), f (x + y) = f x + f y
map_smul'✝¹ :
  ∀ (r : R) (x : M),
    AddHom.toFun { toFun := f, map_add' := map_add'✝¹ } (r • x) =
      ↑(RingHom.id R) r • AddHom.toFun { toFun := f, map_add' := map_add'✝¹ } x
map_lie'✝¹ :
  ∀ {x : L} {m : M},
    AddHom.toFun { toAddHom := { toFun := f, map_add' := map_add'✝¹ }, map_smul' := map_smul'✝¹ }.toAddHom ⁅x, m⁆ =
      ⁅x, AddHom.toFun { toAddHom := { toFun := f, map_add' := map_add'✝¹ }, map_smul' := map_smul'✝¹ }.toAddHom m⁆
g : M → N
map_add'✝ : ∀ (x y : M), g (x + y) = g x + g y
map_smul'✝ :
  ∀ (r : R) (x : M),
    AddHom.toFun { toFun := g, map_add' := map_add'✝ } (r • x) =
      ↑(RingHom.id R) r • AddHom.toFun { toFun := g, map_add' := map_add'✝ } x
map_lie'✝ :
  ∀ {x : L} {m : M},
    AddHom.toFun { toAddHom := { toFun := g, map_add' := map_add'✝ }, map_smul' := map_smul'✝ }.toAddHom ⁅x, m⁆ =
      ⁅x, AddHom.toFun { toAddHom := { toFun := g, map_add' := map_add'✝ }, map_smul' := map_smul'✝ }.toAddHom m⁆
h :
  ↑{ toLinearMap := { toAddHom := { toFun := f, map_add' := map_add'✝¹ }, map_smul' := map_smul'✝¹ },
        map_lie' := map_lie'✝¹ } =
    ↑{ toLinearMap := { toAddHom := { toFun := g, map_add' := map_add'✝ }, map_smul' := map_smul'✝ },
        map_lie' := map_lie'✝ }
⊢ { toLinearMap := { toAddHom := { toFun := f, map_add' := map_add'✝¹ }, map_smul' := map_smul'✝¹ },
      map_lie' := map_lie'✝¹ } =
    { toLinearMap := { toAddHom := { toFun := g, map_add' := map_add'✝ }, map_smul' := map_smul'✝ },
      map_lie' := map_lie'✝ }
R : Type u
L : Type v
M : Type w
N : Type w₁
P : Type w₂
inst✝¹⁴ : CommRing R
inst✝¹³ : LieRing L
inst✝¹² : LieAlgebra R L
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : AddCommGroup N
inst✝⁹ : AddCommGroup P
inst✝⁸ : Module R M
inst✝⁷ : Module R N
inst✝⁶ : Module R P
inst✝⁵ : LieRingModule L M
inst✝⁴ : LieRingModule L N
inst✝³ : LieRingModule L P
inst✝² : LieModule R L M
inst✝¹ : LieModule R L N
inst✝ : LieModule R L P
⊢ Injective FunLike.coe
rintro ⟨⟨⟨f, _⟩⟩⟩ ⟨⟨⟨g, _⟩⟩⟩ h
no goals
case mk.mk.mk.mk.mk.mk
R : Type u
L : Type v
M : Type w
N : Type w₁
P : Type w₂
inst✝¹⁴ : CommRing R
inst✝¹³ : LieRing L
inst✝¹² : LieAlgebra R L
inst✝¹¹ : AddCommGroup M
inst✝¹⁰ : AddCommGroup N
inst✝⁹ : AddCommGroup P
inst✝⁸ : Module R M
inst✝⁷ : Module R N
inst✝⁶ : Module R P
inst✝⁵ : LieRingModule L M
inst✝⁴ : LieRingModule L N
inst✝³ : LieRingModule L P
inst✝² : LieModule R L M
inst✝¹ : LieModule R L N
inst✝ : LieModule R L P
f : M → N
map_add'✝¹ : ∀ (x y : M), f (x + y) = f x + f y
map_smul'✝¹ :
  ∀ (r : R) (x : M),
    AddHom.toFun { toFun := f, map_add' := map_add'✝¹ } (r • x) =
      ↑(RingHom.id R) r • AddHom.toFun { toFun := f, map_add' := map_add'✝¹ } x
map_lie'✝¹ :
  ∀ {x : L} {m : M},
    AddHom.toFun { toAddHom := { toFun := f, map_add' := map_add'✝¹ }, map_smul' := map_smul'✝¹ }.toAddHom ⁅x, m⁆ =
      ⁅x, AddHom.toFun { toAddHom := { toFun := f, map_add' := map_add'✝¹ }, map_smul' := map_smul'✝¹ }.toAddHom m⁆
g : M → N
map_add'✝ : ∀ (x y : M), g (x + y) = g x + g y
map_smul'✝ :
  ∀ (r : R) (x : M),
    AddHom.toFun { toFun := g, map_add' := map_add'✝ } (r • x) =
      ↑(RingHom.id R) r • AddHom.toFun { toFun := g, map_add' := map_add'✝ } x
map_lie'✝ :
  ∀ {x : L} {m : M},
    AddHom.toFun { toAddHom := { toFun := g, map_add' := map_add'✝ }, map_smul' := map_smul'✝ }.toAddHom ⁅x, m⁆ =
      ⁅x, AddHom.toFun { toAddHom := { toFun := g, map_add' := map_add'✝ }, map_smul' := map_smul'✝ }.toAddHom m⁆
h :
  ↑{ toLinearMap := { toAddHom := { toFun := f, map_add' := map_add'✝¹ }, map_smul' := map_smul'✝¹ },
        map_lie' := map_lie'✝¹ } =
    ↑{ toLinearMap := { toAddHom := { toFun := g, map_add' := map_add'✝ }, map_smul' := map_smul'✝ },
        map_lie' := map_lie'✝ }
⊢ { toLinearMap := { toAddHom := { toFun := f, map_add' := map_add'✝¹ }, map_smul' := map_smul'✝¹ },
      map_lie' := map_lie'✝¹ } =
    { toLinearMap := { toAddHom := { toFun := g, map_add' := map_add'✝ }, map_smul' := map_smul'✝ },
      map_lie' := map_lie'✝ }
congr