instance : MulSemiringActionHomClass (R →+*[M] S) M R S where
  coe m := m.toFun
  coe_injective' f g h := by
    rcases f with ⟨⟨tF, _, _⟩, _, _⟩; rcases g with ⟨⟨tG, _, _⟩, _, _⟩
    cases tF; cases tG; 

Proof state:
case mk.mk.mk.mk.mk.mk
M' : Type u_1
X : Type u_2
inst✝²³ : SMul M' X
Y : Type u_3
inst✝²² : SMul M' Y
Z : Type u_4
inst✝²¹ : SMul M' Z
M : Type u_5
inst✝²⁰ : Monoid M
A : Type u_6
inst✝¹⁹ : AddMonoid A
inst✝¹⁸ : DistribMulAction M A
A' : Type u_7
inst✝¹⁷ : AddGroup A'
inst✝¹⁶ : DistribMulAction M A'
B : Type u_8
inst✝¹⁵ : AddMonoid B
inst✝¹⁴ : DistribMulAction M B
B' : Type u_9
inst✝¹³ : AddGroup B'
inst✝¹² : DistribMulAction M B'
C : Type u_10
inst✝¹¹ : AddMonoid C
inst✝¹⁰ : DistribMulAction M C
R : Type u_11
inst✝⁹ : Semiring R
inst✝⁸ : MulSemiringAction M R
R' : Type u_12
inst✝⁷ : Ring R'
inst✝⁶ : MulSemiringAction M R'
S : Type u_13
inst✝⁵ : Semiring S
inst✝⁴ : MulSemiringAction M S
S' : Type u_14
inst✝³ : Ring S'
inst✝² : MulSemiringAction M S'
T : Type u_15
inst✝¹ : Semiring T
inst✝ : MulSemiringAction M T
toFun✝¹ : R → S
map_smul'✝¹ : ∀ (m : M) (x : R), toFun✝¹ (m • x) = m • toFun✝¹ x
map_zero'✝¹ : MulActionHom.toFun { toFun := toFun✝¹, map_smul' := map_smul'✝¹ } 0 = 0
map_add'✝¹ :
  ∀ (x y : R),
    MulActionHom.toFun { toFun := toFun✝¹, map_smul' := map_smul'✝¹ } (x + y) =
      MulActionHom.toFun { toFun := toFun✝¹, map_smul' := map_smul'✝¹ } x +
        MulActionHom.toFun { toFun := toFun✝¹, map_smul' := map_smul'✝¹ } y
map_one'✝¹ :
  MulActionHom.toFun
      { toMulActionHom := { toFun := toFun✝¹, map_smul' := map_smul'✝¹ }, map_zero' := map_zero'✝¹,
          map_add' := map_add'✝¹ }.toMulActionHom
      1 =
    1
map_mul'✝¹ :
  ∀ (x y : R),
    MulActionHom.toFun
        { toMulActionHom := { toFun := toFun✝¹, map_smul' := map_smul'✝¹ }, map_zero' := map_zero'✝¹,
            map_add' := map_add'✝¹ }.toMulActionHom
        (x * y) =
      MulActionHom.toFun
          { toMulActionHom := { toFun := toFun✝¹, map_smul' := map_smul'✝¹ }, map_zero' := map_zero'✝¹,
              map_add' := map_add'✝¹ }.toMulActionHom
          x *
        MulActionHom.toFun
          { toMulActionHom := { toFun := toFun✝¹, map_smul' := map_smul'✝¹ }, map_zero' := map_zero'✝¹,
              map_add' := map_add'✝¹ }.toMulActionHom
          y
toFun✝ : R → S
map_smul'✝ : ∀ (m : M) (x : R), toFun✝ (m • x) = m • toFun✝ x
map_zero'✝ : MulActionHom.toFun { toFun := toFun✝, map_smul' := map_smul'✝ } 0 = 0
map_add'✝ :
  ∀ (x y : R),
    MulActionHom.toFun { toFun := toFun✝, map_smul' := map_smul'✝ } (x + y) =
      MulActionHom.toFun { toFun := toFun✝, map_smul' := map_smul'✝ } x +
        MulActionHom.toFun { toFun := toFun✝, map_smul' := map_smul'✝ } y
map_one'✝ :
  MulActionHom.toFun
      { toMulActionHom := { toFun := toFun✝, map_smul' := map_smul'✝ }, map_zero' := map_zero'✝,
          map_add' := map_add'✝ }.toMulActionHom
      1 =
    1
map_mul'✝ :
  ∀ (x y : R),
    MulActionHom.toFun
        { toMulActionHom := { toFun := toFun✝, map_smul' := map_smul'✝ }, map_zero' := map_zero'✝,
            map_add' := map_add'✝ }.toMulActionHom
        (x * y) =
      MulActionHom.toFun
          { toMulActionHom := { toFun := toFun✝, map_smul' := map_smul'✝ }, map_zero' := map_zero'✝,
              map_add' := map_add'✝ }.toMulActionHom
          x *
        MulActionHom.toFun
          { toMulActionHom := { toFun := toFun✝, map_smul' := map_smul'✝ }, map_zero' := map_zero'✝,
              map_add' := map_add'✝ }.toMulActionHom
          y
h :
  (fun m => m.toFun)
      {
        toDistribMulActionHom :=
          { toMulActionHom := { toFun := toFun✝¹, map_smul' := map_smul'✝¹ }, map_zero' := map_zero'✝¹,
            map_add' := map_add'✝¹ },
        map_one' := map_one'✝¹, map_mul' := map_mul'✝¹ } =
    (fun m => m.toFun)
      {
        toDistribMulActionHom :=
          { toMulActionHom := { toFun := toFun✝, map_smul' := map_smul'✝ }, map_zero' := map_zero'✝,
            map_add' := map_add'✝ },
        map_one' := map_one'✝, map_mul' := map_mul'✝ }
⊢ {
      toDistribMulActionHom :=
        { toMulActionHom := { toFun := toFun✝¹, map_smul' := map_smul'✝¹ }, map_zero' := map_zero'✝¹,
          map_add' := map_add'✝¹ },
      map_one' := map_one'✝¹, map_mul' := map_mul'✝¹ } =
    {
      toDistribMulActionHom :=
        { toMulActionHom := { toFun := toFun✝, map_smul' := map_smul'✝ }, map_zero' := map_zero'✝,
          map_add' := map_add'✝ },
      map_one' := map_one'✝, map_mul' := map_mul'✝ }

Next tactic:
congr