cases b
case mk
b c : ℤω
x✝ y✝ : ℤ
⊢ add (add { x := x✝, y := y✝ } b) c = add { x := x✝, y := y✝ } (add b c)
case mk.mk
c : ℤω
x✝¹ y✝¹ x✝ y✝ : ℤ
⊢ add (add { x := x✝¹, y := y✝¹ } { x := x✝, y := y✝ }) c = add { x := x✝¹, y := y✝¹ } (add { x := x✝, y := y✝ } c)