Nuprl - Some Definitions

NOTE: The 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

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

bnot Def b == if b false else true fi
Thm* b:. b

bool Def == Unit+Unit
Thm* Type

ifthenelse Def if b t else f fi == dec(b ; t; f)
Thm* b:, A:Type, p,q:A. if b p else q fi A

btrue Def true ==
Thm* true

bfalse Def false ==
Thm* false

assert	`Def b == if b True else False fi` `Thm* b:. b Prop`
not	`Def A == A False` `Thm* (A) Prop`
bnot	`Def b == if b false else true fi` `Thm* b:. b`
bool	`Def == Unit+Unit` `Thm* Type`
ifthenelse	`Def if b t else f fi == dec(b ; t; f)` `Thm* b:, A:Type, p,q:A. if b p else q fi A`
btrue	`Def true ==` `Thm* true`
bfalse	`Def false ==` `Thm* false`