-- The main purpose of this test is to ensure it runs instantly!

data Nat : Type where
     Z : Nat
     S : Nat -> Nat

plus : Nat -> Nat -> Nat
plus Z     y = y
plus (S k) y = S (plus k y)

mult : Nat -> Nat -> Nat
mult Z y = Z
mult (S k) y = plus y (mult k y)

five : Nat
five = S (S (S (S (S Z))))

ten : Nat
ten = plus five five

thousand : Nat
thousand = mult ten (mult ten ten)

tenthousand : Nat
tenthousand = mult ten thousand

fiftythousand : Nat
fiftythousand = mult five tenthousand

hundredthousand : Nat
hundredthousand = mult ten tenthousand

data IsSuc : Nat -> Type where
     Yes : IsSuc (S $k)

nonZero : IsSuc Main.hundredthousand
nonZero = Yes