-- Mathlib/Algebra/Ring/Ext.lean
theorem ext ⦃inst₁ inst₂ : NonAssocRing R⦄
    (h_add : local_hAdd[R, inst₁] = local_hAdd[R, inst₂])
    (h_mul : local_hMul[R, inst₁] = local_hMul[R, inst₂]) :
    inst₁ = inst₂

Proof state:
case mk
R : Type u
inst₂ : NonAssocRing R
toNonUnitalNonAssocRing✝ : NonUnitalNonAssocRing R
toOne✝ : One R
one_mul✝ : ∀ (a : R), 1 * a = a
mul_one✝ : ∀ (a : R), a * 1 = a
toNatCast✝ : NatCast R
natCast_zero✝ : NatCast.natCast 0 = 0
natCast_succ✝ : ∀ (n : ℕ), NatCast.natCast (n + 1) = NatCast.natCast n + 1
toIntCast✝ : IntCast R
intCast_ofNat✝ : ∀ (n : ℕ), IntCast.intCast ↑n = ↑n
intCast_negSucc✝ : ∀ (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)
h_add : HAdd.hAdd = HAdd.hAdd
h_mul : HMul.hMul = HMul.hMul
h₁ : toNonUnitalNonAssocRing = toNonUnitalNonAssocRing
h₂ : toNonAssocSemiring = toNonAssocSemiring
h₃ : toAddCommGroupWithOne = toAddCommGroupWithOne
⊢ mk one_mul✝ mul_one✝ natCast_zero✝ natCast_succ✝ intCast_ofNat✝ intCast_negSucc✝ = inst₂

Tactic:
cases inst₂

Result:
case mk.mk
R : Type u
toNonUnitalNonAssocRing✝¹ : NonUnitalNonAssocRing R
toOne✝¹ : One R
one_mul✝¹ : ∀ (a : R), 1 * a = a
mul_one✝¹ : ∀ (a : R), a * 1 = a
toNatCast✝¹ : NatCast R
natCast_zero✝¹ : NatCast.natCast 0 = 0
natCast_succ✝¹ : ∀ (n : ℕ), NatCast.natCast (n + 1) = NatCast.natCast n + 1
toIntCast✝¹ : IntCast R
intCast_ofNat✝¹ : ∀ (n : ℕ), IntCast.intCast ↑n = ↑n
intCast_negSucc✝¹ : ∀ (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)
toNonUnitalNonAssocRing✝ : NonUnitalNonAssocRing R
toOne✝ : One R
one_mul✝ : ∀ (a : R), 1 * a = a
mul_one✝ : ∀ (a : R), a * 1 = a
toNatCast✝ : NatCast R
natCast_zero✝ : NatCast.natCast 0 = 0
natCast_succ✝ : ∀ (n : ℕ), NatCast.natCast (n + 1) = NatCast.natCast n + 1
toIntCast✝ : IntCast R
intCast_ofNat✝ : ∀ (n : ℕ), IntCast.intCast ↑n = ↑n
intCast_negSucc✝ : ∀ (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)
h_add : HAdd.hAdd = HAdd.hAdd
h_mul : HMul.hMul = HMul.hMul
h₁ : toNonUnitalNonAssocRing = toNonUnitalNonAssocRing
h₂ : toNonAssocSemiring = toNonAssocSemiring
h₃ : toAddCommGroupWithOne = toAddCommGroupWithOne
⊢ mk one_mul✝¹ mul_one✝¹ natCast_zero✝¹ natCast_succ✝¹ intCast_ofNat✝¹ intCast_negSucc✝¹ =
    mk one_mul✝ mul_one✝ natCast_zero✝ natCast_succ✝ intCast_ofNat✝ intCast_negSucc✝

Proof state:
case mk.mk.e_toIntCast
R : Type u
toNonUnitalNonAssocRing✝¹ : NonUnitalNonAssocRing R
toOne✝¹ : One R
one_mul✝¹ : ∀ (a : R), 1 * a = a
mul_one✝¹ : ∀ (a : R), a * 1 = a
toNatCast✝¹ : NatCast R
natCast_zero✝¹ : NatCast.natCast 0 = 0
natCast_succ✝¹ : ∀ (n : ℕ), NatCast.natCast (n + 1) = NatCast.natCast n + 1
toIntCast✝¹ : IntCast R
intCast_ofNat✝¹ : ∀ (n : ℕ), IntCast.intCast ↑n = ↑n
intCast_negSucc✝¹ : ∀ (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)
toNonUnitalNonAssocRing✝ : NonUnitalNonAssocRing R
toOne✝ : One R
one_mul✝ : ∀ (a : R), 1 * a = a
mul_one✝ : ∀ (a : R), a * 1 = a
toNatCast✝ : NatCast R
natCast_zero✝ : NatCast.natCast 0 = 0
natCast_succ✝ : ∀ (n : ℕ), NatCast.natCast (n + 1) = NatCast.natCast n + 1
toIntCast✝ : IntCast R
intCast_ofNat✝ : ∀ (n : ℕ), IntCast.intCast ↑n = ↑n
intCast_negSucc✝ : ∀ (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)
h_add : HAdd.hAdd = HAdd.hAdd
h_mul : HMul.hMul = HMul.hMul
h₁ : toNonUnitalNonAssocRing = toNonUnitalNonAssocRing
h₂ : toNonAssocSemiring = toNonAssocSemiring
h₃ : toAddCommGroupWithOne = toAddCommGroupWithOne
⊢ toIntCast✝¹ = toIntCast✝

Tactic:
injection h₂

Result:
case mk.mk.e_toIntCast
R : Type u
toNonUnitalNonAssocRing✝¹ : NonUnitalNonAssocRing R
toOne✝¹ : One R
one_mul✝¹ : ∀ (a : R), 1 * a = a
mul_one✝¹ : ∀ (a : R), a * 1 = a
toNatCast✝¹ : NatCast R
natCast_zero✝¹ : NatCast.natCast 0 = 0
natCast_succ✝¹ : ∀ (n : ℕ), NatCast.natCast (n + 1) = NatCast.natCast n + 1
toIntCast✝¹ : IntCast R
intCast_ofNat✝¹ : ∀ (n : ℕ), IntCast.intCast ↑n = ↑n
intCast_negSucc✝¹ : ∀ (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)
toNonUnitalNonAssocRing✝ : NonUnitalNonAssocRing R
toOne✝ : One R
one_mul✝ : ∀ (a : R), 1 * a = a
mul_one✝ : ∀ (a : R), a * 1 = a
toNatCast✝ : NatCast R
natCast_zero✝ : NatCast.natCast 0 = 0
natCast_succ✝ : ∀ (n : ℕ), NatCast.natCast (n + 1) = NatCast.natCast n + 1
toIntCast✝ : IntCast R
intCast_ofNat✝ : ∀ (n : ℕ), IntCast.intCast ↑n = ↑n
intCast_negSucc✝ : ∀ (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)
h_add : HAdd.hAdd = HAdd.hAdd
h_mul : HMul.hMul = HMul.hMul
h₁ : toNonUnitalNonAssocRing = toNonUnitalNonAssocRing
h₃ : toAddCommGroupWithOne = toAddCommGroupWithOne
toNonUnitalNonAssocSemiring_eq✝ : NonUnitalNonAssocSemiring.mk ⋯ ⋯ ⋯ ⋯ = NonUnitalNonAssocSemiring.mk ⋯ ⋯ ⋯ ⋯
toOne_eq✝ : toOne = toOne
toNatCast_eq✝ : toNatCast = toNatCast
⊢ toIntCast✝¹ = toIntCast✝

Proof state:
R : Type u
inst₁ inst₂ : NonAssocRing R
h_add : HAdd.hAdd = HAdd.hAdd
h_mul : HMul.hMul = HMul.hMul
⊢ inst₁ = inst₂

Tactic:
have h₁ : inst₁.toNonUnitalNonAssocRing = inst₂.toNonUnitalNonAssocRing := by
  ext : 1 <;> assumption

Result:
R : Type u
inst₁ inst₂ : NonAssocRing R
h_add : HAdd.hAdd = HAdd.hAdd
h_mul : HMul.hMul = HMul.hMul
h₁ : toNonUnitalNonAssocRing = toNonUnitalNonAssocRing
⊢ inst₁ = inst₂

Proof state:
case mk.mk.e_toIntCast
R : Type u
toNonUnitalNonAssocRing✝¹ : NonUnitalNonAssocRing R
toOne✝¹ : One R
one_mul✝¹ : ∀ (a : R), 1 * a = a
mul_one✝¹ : ∀ (a : R), a * 1 = a
toNatCast✝¹ : NatCast R
natCast_zero✝¹ : NatCast.natCast 0 = 0
natCast_succ✝¹ : ∀ (n : ℕ), NatCast.natCast (n + 1) = NatCast.natCast n + 1
toIntCast✝¹ : IntCast R
intCast_ofNat✝¹ : ∀ (n : ℕ), IntCast.intCast ↑n = ↑n
intCast_negSucc✝¹ : ∀ (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)
toNonUnitalNonAssocRing✝ : NonUnitalNonAssocRing R
toOne✝ : One R
one_mul✝ : ∀ (a : R), 1 * a = a
mul_one✝ : ∀ (a : R), a * 1 = a
toNatCast✝ : NatCast R
natCast_zero✝ : NatCast.natCast 0 = 0
natCast_succ✝ : ∀ (n : ℕ), NatCast.natCast (n + 1) = NatCast.natCast n + 1
toIntCast✝ : IntCast R
intCast_ofNat✝ : ∀ (n : ℕ), IntCast.intCast ↑n = ↑n
intCast_negSucc✝ : ∀ (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)
h_add : HAdd.hAdd = HAdd.hAdd
h_mul : HMul.hMul = HMul.hMul
h₁ : toNonUnitalNonAssocRing = toNonUnitalNonAssocRing
h₂ : toNonAssocSemiring = toNonAssocSemiring
h₃ : toAddCommGroupWithOne = toAddCommGroupWithOne
⊢ toIntCast✝¹ = toIntCast✝

Tactic:
injection h₃

Result:
no goals

Proof state:
R : Type u
inst₁ inst₂ : NonAssocRing R
h_add : HAdd.hAdd = HAdd.hAdd
h_mul : HMul.hMul = HMul.hMul
h₁ : toNonUnitalNonAssocRing = toNonUnitalNonAssocRing
⊢ inst₁ = inst₂

Tactic:
have h₂ : inst₁.toNonAssocSemiring = inst₂.toNonAssocSemiring := by
  ext : 1 <;> assumption

Result:
R : Type u
inst₁ inst₂ : NonAssocRing R
h_add : HAdd.hAdd = HAdd.hAdd
h_mul : HMul.hMul = HMul.hMul
h₁ : toNonUnitalNonAssocRing = toNonUnitalNonAssocRing
h₂ : toNonAssocSemiring = toNonAssocSemiring
⊢ inst₁ = inst₂

Proof state:
R : Type u
inst₁ inst₂ : NonAssocRing R
h_add : HAdd.hAdd = HAdd.hAdd
h_mul : HMul.hMul = HMul.hMul
h₁ : toNonUnitalNonAssocRing = toNonUnitalNonAssocRing
h₂ : toNonAssocSemiring = toNonAssocSemiring
h₃ : toAddCommGroupWithOne = toAddCommGroupWithOne
⊢ inst₁ = inst₂

Tactic:
cases inst₁

Result:
case mk
R : Type u
inst₂ : NonAssocRing R
toNonUnitalNonAssocRing✝ : NonUnitalNonAssocRing R
toOne✝ : One R
one_mul✝ : ∀ (a : R), 1 * a = a
mul_one✝ : ∀ (a : R), a * 1 = a
toNatCast✝ : NatCast R
natCast_zero✝ : NatCast.natCast 0 = 0
natCast_succ✝ : ∀ (n : ℕ), NatCast.natCast (n + 1) = NatCast.natCast n + 1
toIntCast✝ : IntCast R
intCast_ofNat✝ : ∀ (n : ℕ), IntCast.intCast ↑n = ↑n
intCast_negSucc✝ : ∀ (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)
h_add : HAdd.hAdd = HAdd.hAdd
h_mul : HMul.hMul = HMul.hMul
h₁ : toNonUnitalNonAssocRing = toNonUnitalNonAssocRing
h₂ : toNonAssocSemiring = toNonAssocSemiring
h₃ : toAddCommGroupWithOne = toAddCommGroupWithOne
⊢ mk one_mul✝ mul_one✝ natCast_zero✝ natCast_succ✝ intCast_ofNat✝ intCast_negSucc✝ = inst₂