Nuprl - Some Definitions

accept_list	`Def DA(l) == FinalState(DA)(Result(DA)l)` `Thm* Alph,St:Type, A:Automata(Alph;St), l:Alph*. A(l)`
DA_fin	`Def FinalState(a) == 2of(2of(a))` `Thm* Alph,States:Type, a:Automata(Alph;States). FinalState(a) States`
assert	`Def b == if b True else False fi` `Thm* b:. b Prop`
automata	`Def Automata(Alph;States) == (StatesAlphStates)States(States)` `Thm* Alph,States:Type{i}. Automata(Alph;States) Type{i'}`
compute_list	`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`
iff	`Def P Q == (P Q) & (P Q)` `Thm* A,B:Prop. (A B) Prop`
lang_auto	`Def A(g) == < (s,a. a.s),nil,g >` `Thm* Alph:Type, L:LangOver(Alph), g:((x,y:Alph//(x L-induced Equiv y))). A(g) Automata(Alph;x,y:Alph//(x L-induced Equiv y))`
DA_init	`Def InitialState(a) == 1of(2of(a))` `Thm* Alph,States:Type, a:Automata(Alph;States). InitialState(a) States`
pi2	`Def 2of(t) == t.2` `Thm* A:Type, B:(AType), p:a:AB(a). 2of(p) B(1of(p))`
hd	`Def hd(l) == Case of l; nil "?" ; h.t h` `Thm* A:Type, l:A*. \|\|l\|\|1 hd(l) A`
tl	`Def tl(l) == Case of l; nil nil ; h.t t` `Thm* A:Type, l:A. tl(l) A`
DA_act	`Def a == 1of(a)` `Thm* Alph,States:Type, a:Automata(Alph;States). a StatesAlphStates`
null	`Def null(as) == Case of as; nil true ; a.as' false Thm* T:Type, as:T. null(as)` `Thm null(nil)`
rev_implies	`Def P Q == Q P` `Thm* A,B:Prop. (A B) Prop`
pi1	`Def 1of(t) == t.1` `Thm* A:Type, B:(AType), p:a:AB(a). 1of(p) A`

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