Def ||e:L|| == if null(L)0 ;e=hd(L)1+||e:tl(L)|| else ||e:tl(L)|| fi (recursive)

Thm* n:, L:*. ||n:L||

Def (Ln) == if n=0 nil else (Ln-1) @ L fi (recursive)

Thm* Alph:Type, L:Alph*, n:. (Ln) Alph*

Def == {i:| 0i }

Thm* Type

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

Def i=j == if i=j true ; false fi

Thm* i,j:. i=j

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

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

Thm* null(nil)

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

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

Def AB == B < A

Thm* i,j:. ij Prop

Def A == A False

Thm* A:Prop. (A) Prop