Def ij == ji

Thm* i,j:. ij Prop

Def hd(l) == Case of l; nil "?" ; h.t h

Thm* A:Type, l:A*. ||l||1 hd(l) A

Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive)

Thm* A:Type, l:A*. ||l||

Thm* ||nil||

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 AB == B < A

Thm* i,j:. ij Prop

Def A == A False

Thm* A:Prop. (A) Prop