import hit.pushout open pushout unit bool private definition unit_of_empty (u : empty) : unit := star example : pushout unit_of_empty unit_of_empty → bool := begin intro x, induction x using pushout.rec, exact tt, exact ff, cases x end attribute pushout.rec [recursor] example : pushout unit_of_empty unit_of_empty → bool := begin intro x, induction x, exact tt, exact ff, cases x end