Theorem: Lean4Axiomatic.Integer.neg_inject (Lean4Axiomatic/Integer/Negation.lean)

State before:
ℕ : Type
inst✝⁴ : Natural ℕ
ℤ : Type
inst✝³ : Core ℤ
inst✝² : Addition ℤ
inst✝¹ : Multiplication ℤ
inst✝ : Negation ℤ
a₁ a₂ : ℤ
⊢ -a₁ ≃ -a₂ → a₁ ≃ a₂
Tactic:
intro (_ : -a₁ ≃ -a₂)
State after:
ℕ : Type
inst✝⁴ : Natural ℕ
ℤ : Type
inst✝³ : Core ℤ
inst✝² : Addition ℤ
inst✝¹ : Multiplication ℤ
inst✝ : Negation ℤ
a₁ a₂ : ℤ
x✝ : -a₁ ≃ -a₂
⊢ a₁ ≃ a₂

State before:
ℕ : Type
inst✝⁴ : Natural ℕ
ℤ : Type
inst✝³ : Core ℤ
inst✝² : Addition ℤ
inst✝¹ : Multiplication ℤ
inst✝ : Negation ℤ
a₁ a₂ : ℤ
x✝ : -a₁ ≃ -a₂
⊢ a₁ ≃ a₂
Tactic:
calc
  a₁       ≃ _ := Rel.symm neg_involutive
  (-(-a₁)) ≃ _ := AA.subst₁ ‹-a₁ ≃ -a₂›
  (-(-a₂)) ≃ _ := neg_involutive
  a₂       ≃ _ := Rel.refl
State after:
no goals