constructor
a b : Nat
x✝ : succ a ≤ b
w : Nat
pw : b = succ a + w
⊢ a ≤ b ∧ ¬b ≤ a
case left
a b : Nat
x✝ : succ a ≤ b
w : Nat
pw : b = succ a + w
⊢ a ≤ b

case right
a b : Nat
x✝ : succ a ≤ b
w : Nat
pw : b = succ a + w
⊢ ¬b ≤ a