theorem ex1 (a : Int) (b c : Nat) : a = ↑b - ↑c := sorry

#check ex1

theorem ex2 (a : Int) (b c : Nat) : a = b - c := sorry

#check ex2

theorem ex3 (a : Int) (b c : Nat) : a = ↑(b - c) := sorry

#check ex3