Module: Mathlib.Algebra.Category.ModuleCat.ChangeOfRings

Goal state before:
pp: case add
R✝ : Type u₁
S✝ : Type u₂
inst✝³ : CommRing R✝
inst✝² : CommRing S✝
f✝ : R✝ →+* S✝
R : Type u₁
S : Type u₂
inst✝¹ : CommRing R
inst✝ : CommRing S
f : R →+* S
Y : ModuleCat S
s : S
m1 : Module R S := Module.compHom S f
m2 : Module R ↑Y := Module.compHom (↑Y) f
x✝ y✝ : ↑((restrictScalars f).obj (of S S)) ⊗[R] ↑((restrictScalars f).obj Y)
ih1 :
  (lift { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯, map_smul' := ⋯ })
      (s • x✝) =
    (RingHom.id S) s •
      (lift
          { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯, map_smul' := ⋯ })
        x✝
ih2 :
  (lift { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯, map_smul' := ⋯ })
      (s • y✝) =
    (RingHom.id S) s •
      (lift
          { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯, map_smul' := ⋯ })
        y✝
⊢ (RingHom.id S) s •
        (lift
            { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯,
              map_smul' := ⋯ })
          x✝ +
      (lift
          { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯, map_smul' := ⋯ })
        (s • y✝) =
    (RingHom.id S) s •
      ((lift
            { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯,
              map_smul' := ⋯ })
          x✝ +
        (lift
            { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯,
              map_smul' := ⋯ })
          y✝)

Tactic:
ih2,

Goal state after:
case add
R✝ : Type u₁
S✝ : Type u₂
inst✝³ : CommRing R✝
inst✝² : CommRing S✝
f✝ : R✝ →+* S✝
R : Type u₁
S : Type u₂
inst✝¹ : CommRing R
inst✝ : CommRing S
f : R →+* S
Y : ModuleCat S
s : S
m1 : Module R S := Module.compHom S f
m2 : Module R ↑Y := Module.compHom (↑Y) f
x✝ y✝ : ↑((restrictScalars f).obj (of S S)) ⊗[R] ↑((restrictScalars f).obj Y)
ih1 :
  (lift { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯, map_smul' := ⋯ })
      (s • x✝) =
    (RingHom.id S) s •
      (lift
          { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯, map_smul' := ⋯ })
        x✝
ih2 :
  (lift { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯, map_smul' := ⋯ })
      (s • y✝) =
    (RingHom.id S) s •
      (lift
          { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯, map_smul' := ⋯ })
        y✝
⊢ (RingHom.id S) s •
        (lift
            { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯,
              map_smul' := ⋯ })
          x✝ +
      (RingHom.id S) s •
        (lift
            { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯,
              map_smul' := ⋯ })
          y✝ =
    (RingHom.id S) s •
      ((lift
            { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯,
              map_smul' := ⋯ })
          x✝ +
        (lift
            { toFun := fun s ↦ { toFun := fun y ↦ s • y, map_add' := ⋯, map_smul' := ⋯ }, map_add' := ⋯,
              map_smul' := ⋯ })
          y✝)