Nuprl - Some Definitions

DA_act	`Def a == 1of(a)` `Thm* Alph,States:Type, a:Automata(Alph;States). a StatesAlphStates`
DA_fin	`Def FinalState(a) == 2of(2of(a))` `Thm* Alph,States:Type, a:Automata(Alph;States). FinalState(a) States`
DA_init	`Def InitialState(a) == 1of(2of(a))` `Thm* Alph,States:Type, a:Automata(Alph;States). InitialState(a) States`
automata	`Def Automata(Alph;States) == (StatesAlphStates)States(States)` `Thm* Alph,States:Type{i}. Automata(Alph;States) Type{i'}`
biject	`Def Bij(A; B; f) == Inj(A; B; f) & Surj(A; B; f)` `Thm* A,B:Type, f:(AB). Bij(A; B; f) Prop`
inv_funs	`Def InvFuns(A; B; f; g) == g o f = Id & f o g = Id` `Thm* A,B:Type, f:(AB), g:(BA). InvFuns(A; B; f; g) Prop`
pi1	`Def 1of(t) == t.1` `Thm* A:Type, B:(AType), p:a:AB(a). 1of(p) A`
pi2	`Def 2of(t) == t.2` `Thm* A:Type, B:(AType), p:a:AB(a). 2of(p) B(1of(p))`
surject	`Def Surj(A; B; f) == b:B. a:A. f(a) = b` `Thm* A,B:Type, f:(AB). Surj(A; B; f) Prop`
inject	`Def Inj(A; B; f) == a1,a2:A. f(a1) = f(a2) B a1 = a2` `Thm* A,B:Type, f:(AB). Inj(A; B; f) Prop`
tidentity	`Def Id == Id` `Thm* A:Type. Id AA`
compose	`Def (f o g)(x) == f(g(x))` `Thm* A,B,C:Type, f:(BC), g:(AB). f o g AC`
identity	`Def Id(x) == x` `Thm* A:Type. Id AA`

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