mirror of
https://github.com/idris-lang/Idris2.git
synced 2024-12-26 21:23:53 +03:00
30 lines
678 B
Idris
30 lines
678 B
Idris
fiveIsFive : 5 = 5
|
|
fiveIsFive = Refl
|
|
|
|
twoPlusTwo : 2 + 2 = 4
|
|
twoPlusTwo = Refl
|
|
|
|
-- twoPlusTwoBad : 2 + 2 = 5
|
|
-- twoPlusTwoBad = Refl
|
|
|
|
disjoint : (n : Nat) -> Z = S n -> Void
|
|
disjoint n prf = replace {p = disjointTy} prf ()
|
|
where
|
|
disjointTy : Nat -> Type
|
|
disjointTy Z = ()
|
|
disjointTy (S k) = Void
|
|
|
|
plusReduces : (n:Nat) -> plus Z n = n
|
|
plusReduces n = Refl
|
|
|
|
plusReducesR : (n:Nat) -> plus n Z = n
|
|
plusReducesR n = Refl
|
|
|
|
plusReducesZ : (n:Nat) -> n = plus n Z
|
|
plusReducesZ Z = Refl
|
|
plusReducesZ (S k) = cong S (plusReducesZ k)
|
|
|
|
plusReducesS : (n:Nat) -> (m:Nat) -> S (plus n m) = plus n (S m)
|
|
plusReducesS Z m = Refl
|
|
plusReducesS (S k) m = cong S (plusReducesS k m)
|