/-- `maxTrivSubmodule` is functorial. -/
def maxTrivHom (f : M →ₗ⁅R,L⁆ N) : maxTrivSubmodule R L M →ₗ⁅R,L⁆ maxTrivSubmodule R L N where
  toFun m := ⟨f m, fun x =>
    (LieModuleHom.map_lie _ _ _).symm.trans <|
      (congr_arg f (m.property x)).trans (LieModuleHom.map_zero _)⟩
  map_add' m n := by simp [Function.comp_apply]; rfl -- Porting note:
  map_smul' t m := by simp [Function.comp_apply]; rfl -- these two were `by simpa`
  map_lie' {x m} := by 

Proof state:
R : Type u
L : Type v
M : Type w
N : Type w₁
inst✝¹⁰ : CommRing R
inst✝⁹ : LieRing L
inst✝⁸ : LieAlgebra R L
inst✝⁷ : AddCommGroup M
inst✝⁶ : Module R M
inst✝⁵ : LieRingModule L M
inst✝⁴ : LieModule R L M
inst✝³ : AddCommGroup N
inst✝² : Module R N
inst✝¹ : LieRingModule L N
inst✝ : LieModule R L N
f : M →ₗ⁅R,L⁆ N
x : L
m : ↥↑(maxTrivSubmodule R L M)
⊢ AddHom.toFun
      {
          toAddHom :=
            { toFun := fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) },
              map_add' :=
                (_ :
                  ∀ (m n : ↥↑(maxTrivSubmodule R L M)),
                    (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) (m + n) =
                      (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) m +
                        (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) n) },
          map_smul' :=
            (_ :
              ∀ (t : R) (m : ↥↑(maxTrivSubmodule R L M)),
                AddHom.toFun
                    { toFun := fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) },
                      map_add' :=
                        (_ :
                          ∀ (m n : ↥↑(maxTrivSubmodule R L M)),
                            (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) (m + n) =
                              (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) m +
                                (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) n) }
                    (t • m) =
                  (RingHom.id R) t •
                    AddHom.toFun
                      { toFun := fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) },
                        map_add' :=
                          (_ :
                            ∀ (m n : ↥↑(maxTrivSubmodule R L M)),
                              (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) (m + n) =
                                (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) m +
                                  (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) n) }
                      m) }.toAddHom
      ⁅x, m⁆ =
    ⁅x,
      AddHom.toFun
        {
            toAddHom :=
              { toFun := fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) },
                map_add' :=
                  (_ :
                    ∀ (m n : ↥↑(maxTrivSubmodule R L M)),
                      (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) (m + n) =
                        (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) m +
                          (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) n) },
            map_smul' :=
              (_ :
                ∀ (t : R) (m : ↥↑(maxTrivSubmodule R L M)),
                  AddHom.toFun
                      { toFun := fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) },
                        map_add' :=
                          (_ :
                            ∀ (m n : ↥↑(maxTrivSubmodule R L M)),
                              (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) (m + n) =
                                (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) m +
                                  (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) n) }
                      (t • m) =
                    (RingHom.id R) t •
                      AddHom.toFun
                        { toFun := fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) },
                          map_add' :=
                            (_ :
                              ∀ (m n : ↥↑(maxTrivSubmodule R L M)),
                                (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) (m + n) =
                                  (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) m +
                                    (fun m => { val := f ↑m, property := (_ : ∀ (x : L), ⁅x, f ↑m⁆ = 0) }) n) }
                        m) }.toAddHom
        m⁆

Next tactic:
simp