Nuprl - Some Definitions

Thms relation autom 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

int_upper Def {i...} == {j:| ij }
Thm* n:. {n...} Type

refl Def Refl(T;x,y.E(x;y)) == a:T. E(a;a)
Thm* T:Type, E:(TTProp). Refl(T;x,y.E(x,y)) Prop

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

About:

int_seg	`Def {i..j} == {k:\| i k < j }` `Thm* m,n:. {m..n} Type`
int_upper	`Def {i...} == {j:\| ij }` `Thm* n:. {n...} Type`
refl	`Def Refl(T;x,y.E(x;y)) == a:T. E(a;a)` `Thm* T:Type, E:(TTProp). Refl(T;x,y.E(x,y)) Prop`
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`