Def as @ bs == Case of as; nil bs ; a.as' a.(as' @ bs) (recursive)

Thm* T:Type, as,bs:T*. (as @ bs) T*

Def P Q == (P Q) & (P Q)

Thm* A,B:Prop. (A B) Prop

Def mem_f(T;a;bs) == Case of bs; nil False ; b.bs' b = a T mem_f(T;a;bs') (recursive)

Thm* T:Type, a:T, bs:T*. mem_f(T;a;bs) Prop

Def P Q == Q P

Thm* A,B:Prop. (A B) Prop