Nuprl - Some Definitions

Thms automata 5 Sections AutomataTheory Doc

NOTE:

k is just a notation for {0..k

}

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

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

surject Def Surj(A; B; f) == b:B. a:A. f(a) = b
Thm* A,B:Type, f:(AB). Surj(A; B; f) Prop

About:

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`
not	`Def A == A False` `Thm* A:Prop. (A) Prop`
surject	`Def Surj(A; B; f) == b:B. a:A. f(a) = b` `Thm* A,B:Type, f:(AB). Surj(A; B; f) Prop`