Nuprl - Some Definitions

Thms finite sets 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

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

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

nat_plus Def == {i:| 0 < i }
Thm* Type

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))

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

About:

int_seg	`Def {i..j} == {k:\| i k < j }` `Thm* m,n:. {m..n} Type`
lelt	`Def i j < k == ij & j < k`
le	`Def AB == B < A` `Thm* i,j:. ij Prop`
nat_plus	`Def == {i:\| 0 < i }` `Thm* Type`
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))`
not	`Def A == A False` `Thm* A:Prop. (A) Prop`