have hzz : z = 0 := add_right_eq_zero hzw
case intro.intro
a b w z : Nat
hw : b = b + z + w
hz : a = b + z
hw1 : b + (z + w) = b
hzw : z + w = 0
⊢ a = b
case intro.intro
a b w z : Nat
hw : b = b + z + w
hz : a = b + z
hw1 : b + (z + w) = b
hzw : z + w = 0
hzz : z = 0
⊢ a = b