Nuprl - Some Definitions

Thms choice 1 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

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

trans Def Trans x,y:T. E(x;y) == a,b,c:T. E(a;b) E(b;c) E(a;c)
Thm* T:Type, E:(TTProp). Trans x,y:T. E(x,y) Prop

le Def AB == B < A
Thm* i,j:. ij 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`
nat	`Def == {i:\| 0i }` `Thm* Type`
trans	`Def Trans x,y:T. E(x;y) == a,b,c:T. E(a;b) E(b;c) E(a;c)` `Thm* T:Type, E:(TTProp). Trans x,y:T. E(x,y) Prop`
le	`Def AB == B < A` `Thm* i,j:. ij Prop`
not	`Def A == A False` `Thm* A:Prop. (A) Prop`