Theorem: Lean4Axiomatic.Integer.neg_one_negative (Lean4Axiomatic/Integer/Sign.lean)

State before:
ℕ : Type
inst✝⁵ : Natural ℕ
ℤ : Type
inst✝⁴ : Core ℤ
inst✝³ : Addition ℤ
inst✝² : Multiplication ℤ
inst✝¹ : Negation ℤ
inst✝ : Sign ℤ
⊢ Negative (-1)
Tactic:
have : Positive (1:ℕ) := Natural.one_positive
State after:
ℕ : Type
inst✝⁵ : Natural ℕ
ℤ : Type
inst✝⁴ : Core ℤ
inst✝³ : Addition ℤ
inst✝² : Multiplication ℤ
inst✝¹ : Negation ℤ
inst✝ : Sign ℤ
this : Positive 1
⊢ Negative (-1)

State before:
ℕ : Type
inst✝⁵ : Natural ℕ
ℤ : Type
inst✝⁴ : Core ℤ
inst✝³ : Addition ℤ
inst✝² : Multiplication ℤ
inst✝¹ : Negation ℤ
inst✝ : Sign ℤ
this : Positive 1
⊢ Negative (-1)
Tactic:
have : (-1:ℤ) ≃ -(coe (1:ℕ)) := Rel.refl
State after:
ℕ : Type
inst✝⁵ : Natural ℕ
ℤ : Type
inst✝⁴ : Core ℤ
inst✝³ : Addition ℤ
inst✝² : Multiplication ℤ
inst✝¹ : Negation ℤ
inst✝ : Sign ℤ
this✝ : Positive 1
this : -1 ≃ -coe 1
⊢ Negative (-1)

State before:
ℕ : Type
inst✝⁵ : Natural ℕ
ℤ : Type
inst✝⁴ : Core ℤ
inst✝³ : Addition ℤ
inst✝² : Multiplication ℤ
inst✝¹ : Negation ℤ
inst✝ : Sign ℤ
this✝ : Positive 1
this : -1 ≃ -coe 1
⊢ Negative (-1)
Tactic:
have : Negative (-1:ℤ) :=
  negative_intro_nat ‹Positive (1:ℕ)› ‹(-1:ℤ) ≃ -(coe (1:ℕ))›
State after:
ℕ : Type
inst✝⁵ : Natural ℕ
ℤ : Type
inst✝⁴ : Core ℤ
inst✝³ : Addition ℤ
inst✝² : Multiplication ℤ
inst✝¹ : Negation ℤ
inst✝ : Sign ℤ
this✝¹ : Positive 1
this✝ : -1 ≃ -coe 1
this : Negative (-1)
⊢ Negative (-1)

State before:
ℕ : Type
inst✝⁵ : Natural ℕ
ℤ : Type
inst✝⁴ : Core ℤ
inst✝³ : Addition ℤ
inst✝² : Multiplication ℤ
inst✝¹ : Negation ℤ
inst✝ : Sign ℤ
this✝¹ : Positive 1
this✝ : -1 ≃ -coe 1
this : Negative (-1)
⊢ Negative (-1)
Tactic:
exact this
State after:
no goals