exists w'
case succ
a b : Nat
h : a ≤ b ∧ ¬b ≤ a
hc : ¬b ≤ a
w' : Nat
pw : b = a + succ w'
⊢ succ a ≤ b
case succ
a b : Nat
h : a ≤ b ∧ ¬b ≤ a
hc : ¬b ≤ a
w' : Nat
pw : b = a + succ w'
⊢ b = succ a + w'