Module: Mathlib.Order.JordanHolder

Goal state before:
pp: case refine_1
X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s₁ s₂ : CompositionSeries X
x₁ x₂ : X
hsat₁ : IsMaximal (last s₁) x₁
hsat₂ : IsMaximal (last s₂) x₂
hequiv : s₁.Equivalent s₂
hlast : Iso (last s₁, x₁) (last s₂, x₂)
e : Fin s₁.length.succ ≃ Fin s₂.length.succ :=
  Trans.trans (Trans.trans finSuccEquivLast (Functor.mapEquiv Option (Exists.choose hequiv))) finSuccEquivLast.symm
he_last : e (Fin.last s₁.length) = Fin.last s₂.length
he_castSucc : ∀ (j : Fin s₁.length), e j.castSucc = ((Exists.choose hequiv) j).castSucc
i : Fin (snoc s₁ x₁ hsat₁).length
⊢ Iso
    ((snoc s₁ x₁ hsat₁).toFun
        (Fin.last (s₁.length + (RelSeries.singleton {(x, y) | IsMaximal x y} x₁).length)).castSucc,
      (snoc s₁ x₁ hsat₁).toFun (Fin.last (s₁.length + (RelSeries.singleton {(x, y) | IsMaximal x y} x₁).length)).succ)
    ((snoc s₂ x₂ hsat₂).toFun
        (e (Fin.last (s₁.length + (RelSeries.singleton {(x, y) | IsMaximal x y} x₁).length))).castSucc,
      (snoc s₂ x₂ hsat₂).toFun
        (e (Fin.last (s₁.length + (RelSeries.singleton {(x, y) | IsMaximal x y} x₁).length))).succ)

pp: case refine_2
X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s₁ s₂ : CompositionSeries X
x₁ x₂ : X
hsat₁ : IsMaximal (last s₁) x₁
hsat₂ : IsMaximal (last s₂) x₂
hequiv : s₁.Equivalent s₂
hlast : Iso (last s₁, x₁) (last s₂, x₂)
e : Fin s₁.length.succ ≃ Fin s₂.length.succ :=
  Trans.trans (Trans.trans finSuccEquivLast (Functor.mapEquiv Option (Exists.choose hequiv))) finSuccEquivLast.symm
he_last : e (Fin.last s₁.length) = Fin.last s₂.length
he_castSucc : ∀ (j : Fin s₁.length), e j.castSucc = ((Exists.choose hequiv) j).castSucc
i : Fin (snoc s₁ x₁ hsat₁).length
⊢ ∀ (i : Fin (s₁.length + (RelSeries.singleton {(x, y) | IsMaximal x y} x₁).length)),
    Iso ((snoc s₁ x₁ hsat₁).toFun i.castSucc.castSucc, (snoc s₁ x₁ hsat₁).toFun i.castSucc.succ)
      ((snoc s₂ x₂ hsat₂).toFun (e i.castSucc).castSucc, (snoc s₂ x₂ hsat₂).toFun (e i.castSucc).succ)

Tactic:
· change Iso ((snoc s₁ x₁ hsat₁).toFun (Fin.last s₁.length).castSucc,
        (snoc s₁ x₁ hsat₁).toFun (Fin.last s₁.length).succ)
      ((snoc s₂ x₂ hsat₂).toFun (e (Fin.last s₁.length)).castSucc,
        (snoc s₂ x₂ hsat₂).toFun (e (Fin.last s₁.length)).succ)
    rw [he_last]
    simpa [apply_last] using hlast

Goal state after:
case refine_2
X : Type u
inst✝¹ : Lattice X
inst✝ : JordanHolderLattice X
s₁ s₂ : CompositionSeries X
x₁ x₂ : X
hsat₁ : IsMaximal (last s₁) x₁
hsat₂ : IsMaximal (last s₂) x₂
hequiv : s₁.Equivalent s₂
hlast : Iso (last s₁, x₁) (last s₂, x₂)
e : Fin s₁.length.succ ≃ Fin s₂.length.succ :=
  Trans.trans (Trans.trans finSuccEquivLast (Functor.mapEquiv Option (Exists.choose hequiv))) finSuccEquivLast.symm
he_last : e (Fin.last s₁.length) = Fin.last s₂.length
he_castSucc : ∀ (j : Fin s₁.length), e j.castSucc = ((Exists.choose hequiv) j).castSucc
i : Fin (snoc s₁ x₁ hsat₁).length
⊢ ∀ (i : Fin (s₁.length + (RelSeries.singleton {(x, y) | IsMaximal x y} x₁).length)),
    Iso ((snoc s₁ x₁ hsat₁).toFun i.castSucc.castSucc, (snoc s₁ x₁ hsat₁).toFun i.castSucc.succ)
      ((snoc s₂ x₂ hsat₂).toFun (e i.castSucc).castSucc, (snoc s₂ x₂ hsat₂).toFun (e i.castSucc).succ)