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

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

Def l \ a == Case of l; nil nil ; h.l' if eq(a,h) l' \ a else h.(l' \ a) fi (recursive)

Thm* St:Type, l:St*, s:St, eq:(StSt). (l \ s) St*

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