Def C+[a;q] == map(c. < 1of(c),a.2of(c) > ;C) @ [ < q,nil > ]

Thm* Alph,St:Type, C:NComp(Alph;St), a:Alph, q:St. C+[a;q] NComp(Alph;St)

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

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

Def NComp(Alph;St) == {C:(StAlph* List)| i:(||C||-1). ||2of(C[i])|| > 0 }

Thm* Alph,St:Type. NComp(Alph;St) Type

Def T List == {l:(T*)| ||l|| > 0 }

Thm* T:Type. (T List) Type

Thm* i,j:. i > j Prop

Def {i..j} == {k:| i k < j }

Thm* m,n:. {m..n} Type

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

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

Thm* ||nil||

Def map(f;as) == Case of as; nil nil ; a.as' f(a).map(f;as') (recursive)

Thm* A,B:Type, f:(AB), l:A*. map(f;l) B*

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

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

Thm* A:Type, l:A*, n:. 0n n < ||l|| l[n] A

Def nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi (recursive)

Thm* A:Type, as:A*, i:. nth_tl(i;as) A*

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

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

Def AB == B < A

Thm* i,j:. ij Prop

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

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

Def ij == j < i

Thm* i,j:. ij

Def A == A False

Thm* A:Prop. (A) Prop

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

Thm* i,j:. i < j

Def b == if b false else true fi

Thm* b:. b