Nuprl - Some Definitions

Thms myhill nerode Sections AutomataTheory Doc

NOTE: This operator coercing a

to a Prop is normally invisible since it is pretty obvious when it is needed.

assert Def b == if b True else False fi
Thm* b:. b 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

int_seg Def {i..j} == {k:| i k < j }
Thm* m,n:. {m..n} Type

nat Def == {i:| 0i }
Thm* Type

lelt Def i j < k == ij & j < k

le Def AB == B < A
Thm* i,j:. ij Prop

mem_f Def mem_f(T;a;bs) == Case of bs; nil False ; b.bs' b = a T mem_f(T;a;bs') (recursive)
Thm* T:Type, a:T, bs:T*. mem_f(T;a;bs) Prop

not Def A == A False
Thm* A:Prop. (A) Prop

About:

assert	`Def b == if b True else False fi` `Thm* b:. b 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`
int_seg	`Def {i..j} == {k:\| i k < j }` `Thm* m,n:. {m..n} Type`
nat	`Def == {i:\| 0i }` `Thm* Type`
lelt	`Def i j < k == ij & j < k`
le	`Def AB == B < A` `Thm* i,j:. ij Prop`
mem_f	`Def mem_f(T;a;bs) == Case of bs; nil False ; b.bs' b = a T mem_f(T;a;bs') (recursive)` `Thm* T:Type, a:T, bs:T*. mem_f(T;a;bs) Prop`
not	`Def A == A False` `Thm* A:Prop. (A) Prop`