Theorem: Lean4Axiomatic.Integer.neg_one_neqv_zero (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
⊢ -1 ≄ 0
Tactic:
intro (_ : -1 ≃ (0:ℤ))
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
x✝ : -1 ≃ 0
⊢ False

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
x✝ : -1 ≃ 0
⊢ False
Tactic:
have : 1 ≃ (0:ℤ) := calc
  1      ≃ _ := Rel.symm AA.identR
  1 + 0  ≃ _ := AA.substR (Rel.symm ‹-1 ≃ (0:ℤ)›)
  1 + -1 ≃ _ := AA.inverseR
  0      ≃ _ := Rel.refl
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
x✝ : -1 ≃ 0
this : 1 ≃ 0
⊢ False

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
x✝ : -1 ≃ 0
this : 1 ≃ 0
⊢ False
Tactic:
have : (1:ℤ) ≄ 0 := one_neqv_zero
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
x✝ : -1 ≃ 0
this✝ : 1 ≃ 0
this : 1 ≄ 0
⊢ False

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
x✝ : -1 ≃ 0
this✝ : 1 ≃ 0
this : 1 ≄ 0
⊢ False
Tactic:
exact absurd ‹1 ≃ (0:ℤ)› ‹1 ≄ (0:ℤ)›
State after:
no goals