-- Lean 4 proof step from Mathlib.CategoryTheory.Monoidal.Bimod (goal)
Goal:
C : Type u₁
inst : Category.{v₁, u₁} C
inst_1 : MonoidalCategory.{v₁, u₁} C
inst_2 : HasCoequalizers.{v₁, u₁} C
inst_3 : ∀ (X : C), PreservesColimitsOfSize.{0, 0, v₁, v₁, u₁, u₁} (tensorLeft X)
inst_4 : ∀ (X : C), PreservesColimitsOfSize.{0, 0, v₁, v₁, u₁, u₁} (tensorRight X)
R S T U : Mon.{v₁, u₁} C
P : Bimod R S
Q : Bimod S T
L : Bimod T U
⊢ CategoryStruct.comp (Y :=
      tensorObj.{v₁, u₁} (𝒞 := inst) (coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft)) L.X)
      (coequalizer.π (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft) ▷ L.X :
        tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) P.X Q.X) L.X ⟶
          tensorObj.{v₁, u₁} (𝒞 := inst) (coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft))
            L.X)
      (coequalizer.π (TensorBimod.actRight P Q ▷ L.X)
          (Iso.hom (α_ (coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft)) T.X L.X) ≫
            coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft) ◁ L.actLeft) :
        tensorObj.{v₁, u₁} (𝒞 := inst) (coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft))
            L.X ⟶
          coequalizer (TensorBimod.actRight P Q ▷ L.X)
            (Iso.hom (α_ (coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft)) T.X L.X) ≫
              coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft) ◁ L.actLeft)) =
    coequalizer.π (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft) ▷ L.X ≫
      coequalizer.π ((P.tensorBimod Q).actRight ▷ L.X)
          (Iso.hom (α_ (P.tensorBimod Q).X T.X L.X) ≫ (P.tensorBimod Q).X ◁ L.actLeft) ≫
        𝟙
          (coequalizer ((P.tensorBimod Q).actRight ▷ L.X)
            (Iso.hom (α_ (P.tensorBimod Q).X T.X L.X) ≫ (P.tensorBimod Q).X ◁ L.actLeft))
have h : Eq (α :=
  Functor.obj.{v₁, v₁, u₁, u₁} (tensorRight L.X) (tensorObj.{v₁, u₁} (𝒞 := inst) P.X Q.X) ⟶
    coequalizer ((P.tensorBimod Q).actRight ▷ L.X)
      (Iso.hom (α_ (P.tensorBimod Q).X T.X L.X) ≫ (P.tensorBimod Q).X ◁ L.actLeft))
  (CategoryStruct.comp (Y :=
      tensorObj.{v₁, u₁} (𝒞 := inst) (coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft)) L.X)
      (coequalizer.π (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft) ▷ L.X :
        tensorObj.{v₁, u₁} (𝒞 := inst) (tensorObj.{v₁, u₁} (𝒞 := inst) P.X Q.X) L.X ⟶
          tensorObj.{v₁, u₁} (𝒞 := inst) (coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft))
            L.X)
      (coequalizer.π (TensorBimod.actRight P Q ▷ L.X)
          (Iso.hom (α_ (coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft)) T.X L.X) ≫
            coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft) ◁ L.actLeft) :
        tensorObj.{v₁, u₁} (𝒞 := inst) (coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft))
            L.X ⟶
          coequalizer (TensorBimod.actRight P Q ▷ L.X)
            (Iso.hom (α_ (coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft)) T.X L.X) ≫
              coequalizer (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft) ◁ L.actLeft)) :
    Functor.obj.{v₁, v₁, u₁, u₁} (tensorRight L.X) (tensorObj.{v₁, u₁} (𝒞 := inst) P.X Q.X) ⟶
      coequalizer ((P.tensorBimod Q).actRight ▷ L.X)
        (Iso.hom (α_ (P.tensorBimod Q).X T.X L.X) ≫ (P.tensorBimod Q).X ◁ L.actLeft))
  (coequalizer.π (P.actRight ▷ Q.X) (Iso.hom (α_ P.X S.X Q.X) ≫ P.X ◁ Q.actLeft) ▷ L.X ≫
      coequalizer.π ((P.tensorBimod Q).actRight ▷ L.X)
        (Iso.hom (α_ (P.tensorBimod Q).X T.X L.X) ≫ (P.tensorBimod Q).X ◁ L.actLeft) :
    Functor.obj.{v₁, v₁, u₁, u₁} (tensorRight L.X) (tensorObj.{v₁, u₁} (𝒞 := inst) P.X Q.X) ⟶
      coequalizer ((P.tensorBimod Q).actRight ▷ L.X)
        (Iso.hom (α_ (P.tensorBimod Q).X T.X L.X) ≫ (P.tensorBimod Q).X ◁ L.actLeft))
Tactic: slice_rhs 2 3 => rw [Category.comp_id]