partial def fact : Nat → Nat
| 0     => 1
| (n+1) => (n+1)*fact n

#guard fact 10 == 3628800
#guard fact 100 == 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

theorem tst1 : fact 10 = 3628800 :=
  by native_decide

theorem tst2 : fact 100 = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 :=
  by native_decide

theorem tst3 : decide (10000000000000000 < 200000000000000000000) = true :=
  by native_decide

theorem tst4 : 10000000000000000 < 200000000000000000000 :=
  by decide

theorem tst5 : 10000000000000000 < 200000000000000000000 :=
  by native_decide

theorem tst6 : 10000000000000000 < 200000000000000000000 :=
  let h₁ : 10000000000000000 < 10000000000000010 := by native_decide
  let h₂ : 10000000000000010 < 200000000000000000000 := by native_decide
  Nat.lt_trans h₁ h₂

theorem tst7 : 10000000000000000 < 200000000000000000000 :=
  by decide

theorem tst8 : 10000000000000000 < 200000000000000000000 :=
  let h₁ : 10000000000000000 < 10000000000000010 := by decide
  let h₂ : 10000000000000010 < 200000000000000000000 := by decide
  Nat.lt_trans h₁ h₂

theorem tst9 : 10000000000000000 < 200000000000000000000 :=
  by decide

theorem tst10 : 10000000000000000 < 200000000000000000000 :=
  by native_decide
