theorem ex1 (a : α) (b : List α) : (a::b = []) = False :=
  by simp

theorem ex2 (a : α) (b : List α) : (a::b = []) = False :=
  by simp

theorem ex3 (x : Nat) : (if Nat.succ x = 0 then 1 else 2) = 2 :=
  by simp

theorem ex4 (x : Nat) : (if 10 = 0 then 1 else 2) = 2 :=
  by simp

theorem ex5 : (10 = 20) = False :=
  by simp

#print ex5

theorem ex6 : (if "hello" = "world" then 1 else 2) = 2 :=
  by simp

#print ex6

theorem ex7 : (if "hello" = "world" then 1 else 2) = 2 := by
  fail_if_success simp (config := { decide := false })
  simp

theorem ex8 : (10 + 2000 = 20) = False :=
  by simp

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

theorem ex9 : (if fact 100 > 10 then true else false) = true :=
  by simp
