Def (S:Ls) == if null(L) s else S.act(hd(L),(S:tl(L)s)) fi (recursive)

Thm* Alph:Type, S:ActionSet(Alph), L:Alph*, s:S.car. (S:Ls) S.car

Def tl(l) == Case of l; nil nil ; h.t t

Thm* A:Type, l:A*. tl(l) A*

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

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

Thm* T:Type, a:ActionSet(T). a.act Ta.cara.car

Def null(as) == Case of as; nil true ; a.as' false

Thm* T:Type, as:T*. null(as)

Thm* null(nil)

Thm* A:Type, B:(AType), p:a:AB(a). 2of(p) B(1of(p))