intro hm
case left
m n : Nat
disjoint : m &&& n = 0
⊢ m = 0 → m + n = m ^^^ n

case right
m n : Nat
disjoint : m &&& n = 0
⊢ m > 0 → m + n = m ^^^ n
case left
m n : Nat
disjoint : m &&& n = 0
hm : m = 0
⊢ m + n = m ^^^ n

case right
m n : Nat
disjoint : m &&& n = 0
⊢ m > 0 → m + n = m ^^^ n