cases a
a b c : ℤθ
⊢ mul a (add b c) = add (mul a b) (mul a c)
case mk
b c : ℤθ
f✝ g✝ h✝ : ℤ
⊢ mul { f := f✝, g := g✝, h := h✝ } (add b c) =
    add (mul { f := f✝, g := g✝, h := h✝ } b) (mul { f := f✝, g := g✝, h := h✝ } c)