cases b
case mk
b c : ℤα
z✝ w✝ : ℤ
⊢ add (add { z := z✝, w := w✝ } b) c = add { z := z✝, w := w✝ } (add b c)
case mk.mk
c : ℤα
z✝¹ w✝¹ z✝ w✝ : ℤ
⊢ add (add { z := z✝¹, w := w✝¹ } { z := z✝, w := w✝ }) c = add { z := z✝¹, w := w✝¹ } (add { z := z✝, w := w✝ } c)