Nuprl - Some Definitions

decidable	`Def Dec(P) == P P` `Thm* A:Prop. Dec(A) Prop`
iff	`Def P Q == (P Q) & (P Q)` `Thm* A,B:Prop. (A B) Prop`
int_seg	`Def {i..j} == {k:\| i k < j }` `Thm* m,n:. {m..n} Type`
inv_funs	`Def InvFuns(A; B; f; g) == g o f = Id & f o g = Id` `Thm* A,B:Type, f:(AB), g:(BA). InvFuns(A; B; f; g) Prop`
mem_f	`Def mem_f(T;a;bs) == Case of bs; nil False ; b.bs' b = a T mem_f(T;a;bs') (recursive)` `Thm* T:Type, a:T, bs:T*. mem_f(T;a;bs) Prop`
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`
rev_implies	`Def P Q == Q P` `Thm* A,B:Prop. (A B) Prop`
tidentity	`Def Id == Id` `Thm* A:Type. Id AA`
compose	`Def (f o g)(x) == f(g(x))` `Thm* A,B,C:Type, f:(BC), g:(AB). f o g AC`
identity	`Def Id(x) == x` `Thm* A:Type. Id AA`

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