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

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

Def Automata(Alph;States) == (StatesAlphStates)States(States)

Thm* Alph,States:Type{i}. Automata(Alph;States) Type{i'}

Def Result(DA)l == if null(l) InitialState(DA) else DA((Result(DA)tl(l)),hd(l)) fi (recursive)

Thm* Alph,St:Type, A:Automata(Alph;St), l:Alph*. (Result(A)l) St

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

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

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

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

Def a == 1of(a)

Thm* Alph,States:Type, a:Automata(Alph;States). a StatesAlphStates

Thm* Alph,States:Type, a:Automata(Alph;States). InitialState(a) States

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). 1of(p) A

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