have := calc
  (m ^^^ n) &&& n
    = (m &&& n) ^^^ (n &&& n) := Nat.xor_and m n n
  _ = n ^^^ n := by rw [incl, Nat.land_self n]
  _ = 0 := Nat.xor_self n
case h
m n : Nat
incl : m &&& n = n
⊢ m = (m ^^^ n) + n
case h
m n : Nat
incl : m &&& n = n
this : (m ^^^ n) &&& n = 0
⊢ m = (m ^^^ n) + n