-- Module: Mathlib.Algebra.Ring.Ext
Goal:
R : Type u
inst₂ : AddGroupWithOne R
toAddMonoidWithOne : AddMonoidWithOne R
toNeg : Neg R
toSub : Sub R
sub_eq_add_neg : ∀ (a b : R), a - b = a + -b
zsmul : ℤ → R → R
zsmul_zero' : ∀ (a : R), zsmul 0 a = 0
zsmul_succ' : ∀ (n : ℕ) (a : R), zsmul (↑n.succ : ℤ) a = zsmul (↑n : ℤ) a + a
zsmul_neg' : ∀ (n : ℕ) (a : R), zsmul (Int.negSucc n) a = -zsmul (↑n.succ : ℤ) a
neg_add_cancel : ∀ (a : R), -a + a = 0
intCast : ℤ → R
intCast_ofNat : ∀ (n : ℕ), Eq.{u + 1} (α := R) (IntCast.intCast (↑n : ℤ)) (↑n : R)
intCast_negSucc : ∀ (n : ℕ), Eq.{u + 1} (α := R) (IntCast.intCast (Int.negSucc n)) (-(↑(n + 1) : R))
h_add : Eq (α := R → R → R) HAdd.hAdd HAdd.hAdd
h_one : Eq.{u + 1} (α := R) One.one One.one
this_1 : Eq.{u + 1} (α := AddMonoidWithOne R) AddGroupWithOne.toAddMonoidWithOne AddGroupWithOne.toAddMonoidWithOne
this_2 : Eq.{u + 1} (α := NatCast R) AddMonoidWithOne.toNatCast AddMonoidWithOne.toNatCast
toAddMonoid_eq : Eq.{u + 1} (α := AddMonoid R) AddMonoidWithOne.toAddMonoid AddMonoidWithOne.toAddMonoid
toNeg_eq : Eq.{u + 1} (α := Neg R) AddGroupWithOne.toNeg AddGroupWithOne.toNeg
toSub_eq : Eq.{u + 1} (α := Sub R) AddGroupWithOne.toSub AddGroupWithOne.toSub
zsmul_eq : Eq.{u + 1} (α := ℤ → R → R) AddGroupWithOne.zsmul AddGroupWithOne.zsmul
this : Eq.{u + 1} (α := ℤ → R) IntCast.intCast IntCast.intCast
rcases :
  ∀ [toAddMonoidWithOne_1 : AddMonoidWithOne R] [toNeg_1 : Neg R] [toSub_1 : Sub R]
    (sub_eq_add_neg_1 : ∀ (a b : R), a - b = a + -b) (zsmul_1 : ℤ → R → R) (zsmul_zero'_1 : ∀ (a : R), zsmul_1 0 a = 0)
    (zsmul_succ'_1 : ∀ (n : ℕ) (a : R), zsmul_1 (↑n.succ : ℤ) a = zsmul_1 (↑n : ℤ) a + a)
    (zsmul_neg'_1 : ∀ (n : ℕ) (a : R), zsmul_1 (Int.negSucc n) a = -zsmul_1 (↑n.succ : ℤ) a)
    (neg_add_cancel_1 : ∀ (a : R), -a + a = 0) (intCast_1 : ℤ → R)
    (intCast_ofNat_1 : ∀ (n : ℕ), Eq.{u + 1} (α := R) (IntCast.intCast (↑n : ℤ)) (↑n : R))
    (intCast_negSucc_1 : ∀ (n : ℕ), Eq.{u + 1} (α := R) (IntCast.intCast (Int.negSucc n)) (-(↑(n + 1) : R)))
    (h_add : Eq (α := R → R → R) HAdd.hAdd HAdd.hAdd) (h_one : Eq.{u + 1} (α := R) One.one One.one)
    (this : Eq.{u + 1} (α := AddMonoidWithOne R) AddGroupWithOne.toAddMonoidWithOne AddGroupWithOne.toAddMonoidWithOne)
    (this : Eq.{u + 1} (α := NatCast R) AddMonoidWithOne.toNatCast AddMonoidWithOne.toNatCast),
    Eq.{u + 1} (α := AddMonoid R) AddMonoidWithOne.toAddMonoid AddMonoidWithOne.toAddMonoid →
      Eq.{u + 1} (α := Neg R) AddGroupWithOne.toNeg AddGroupWithOne.toNeg →
        Eq.{u + 1} (α := Sub R) AddGroupWithOne.toSub AddGroupWithOne.toSub →
          Eq.{u + 1} (α := ℤ → R → R) AddGroupWithOne.zsmul AddGroupWithOne.zsmul →
            ∀ (this : Eq.{u + 1} (α := ℤ → R) IntCast.intCast IntCast.intCast),
              { intCast := intCast, toAddMonoidWithOne := toAddMonoidWithOne, toNeg := toNeg, toSub := toSub,
                  sub_eq_add_neg := sub_eq_add_neg, zsmul := zsmul, zsmul_zero' := zsmul_zero',
                  zsmul_succ' := zsmul_succ', zsmul_neg' := zsmul_neg', neg_add_cancel := neg_add_cancel,
                  intCast_ofNat := intCast_ofNat, intCast_negSucc := intCast_negSucc : AddGroupWithOne R } =
                { intCast := intCast_1, toAddMonoidWithOne := toAddMonoidWithOne_1, toNeg := toNeg_1, toSub := toSub_1,
                  sub_eq_add_neg := sub_eq_add_neg_1, zsmul := zsmul_1, zsmul_zero' := zsmul_zero'_1,
                  zsmul_succ' := zsmul_succ'_1, zsmul_neg' := zsmul_neg'_1, neg_add_cancel := neg_add_cancel_1,
                  intCast_ofNat := intCast_ofNat_1, intCast_negSucc := intCast_negSucc_1 }
⊢ { intCast := intCast, toAddMonoidWithOne := toAddMonoidWithOne, toNeg := toNeg, toSub := toSub,
      sub_eq_add_neg := sub_eq_add_neg, zsmul := zsmul, zsmul_zero' := zsmul_zero', zsmul_succ' := zsmul_succ',
      zsmul_neg' := zsmul_neg', neg_add_cancel := neg_add_cancel, intCast_ofNat := intCast_ofNat,
      intCast_negSucc := intCast_negSucc : AddGroupWithOne R } =
    inst₂

Tactic:
rcases inst₂ with @⟨⟨⟩⟩