16 lines
390 B
Text
16 lines
390 B
Text
import logic
|
||
|
||
inductive Three :=
|
||
zero : Three,
|
||
one : Three,
|
||
two : Three
|
||
|
||
namespace Three
|
||
|
||
theorem disj (a : Three) : a = zero ∨ a = one ∨ a = two :=
|
||
rec (or.inl rfl) (or.inr (or.inl rfl)) (or.inr (or.inr rfl)) a
|
||
|
||
example (a : Three) : a ≠ zero → a ≠ one → a = two :=
|
||
rec (λ h₁ h₂, absurd rfl h₁) (λ h₁ h₂, absurd rfl h₂) (λ h₁ h₂, rfl) a
|
||
|
||
end Three
|