Theorem: Lean4Axiomatic.Integer.signs_distinct (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
a : ℤ
⊢ ¬AA.TwoOfThree (a ≃ 0) (a ≃ 1) (a ≃ -1)
Tactic:
intro (two : AA.TwoOfThree (a ≃ 0) (a ≃ 1) (a ≃ -1))
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
a : ℤ
two : AA.TwoOfThree (a ≃ 0) (a ≃ 1) (a ≃ -1)
⊢ 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
a : ℤ
two : AA.TwoOfThree (a ≃ 0) (a ≃ 1) (a ≃ -1)
⊢ False
Tactic:
match two with
| AA.TwoOfThree.oneAndTwo (_ : a ≃ 0) (_ : a ≃ 1) =>
  exact Rel.trans_failR ‹a ≃ 1› one_neqv_zero ‹a ≃ 0›
| AA.TwoOfThree.oneAndThree (_ : a ≃ 0) (_ : a ≃ -1) =>
  exact Rel.trans_failR ‹a ≃ -1› neg_one_neqv_zero ‹a ≃ 0›
| AA.TwoOfThree.twoAndThree (_ : a ≃ 1) (_ : a ≃ -1) =>
  exact Rel.trans_failR ‹a ≃ -1› neg_one_neqv_one ‹a ≃ 1›
State after:
no goals

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
a : ℤ
two : AA.TwoOfThree (a ≃ 0) (a ≃ 1) (a ≃ -1)
a✝ : a ≃ 0
b✝ : a ≃ 1
⊢ False
Tactic:
exact Rel.trans_failR ‹a ≃ 1› one_neqv_zero ‹a ≃ 0›
State after:
no goals

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
a : ℤ
two : AA.TwoOfThree (a ≃ 0) (a ≃ 1) (a ≃ -1)
a✝ : a ≃ 0
c✝ : a ≃ -1
⊢ False
Tactic:
exact Rel.trans_failR ‹a ≃ -1› neg_one_neqv_zero ‹a ≃ 0›
State after:
no goals

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
a : ℤ
two : AA.TwoOfThree (a ≃ 0) (a ≃ 1) (a ≃ -1)
b✝ : a ≃ 1
c✝ : a ≃ -1
⊢ False
Tactic:
exact Rel.trans_failR ‹a ≃ -1› neg_one_neqv_one ‹a ≃ 1›
State after:
no goals