Nuprl - Some Definitions

turing_machine	`Def TM(M) == Finite((M)) & Finite((M)) & Finite((M)) & M.t = M.r` `Thm* M:PM{i}. TM(M) Prop`
tm_r	`Def p.r == 2of(2of(2of(2of(2of(2of(2of(p)))))))` `Thm* p:PM{i}. p.r (p)`
tm_t	`Def p.t == 1of(2of(2of(2of(2of(2of(2of(p)))))))` `Thm* p:PM{i}. p.t (p)`
tm_q	`Def (p) == 1of(p)` `Thm* p:PM{i}. (p) Type`
finite	`Def Finite(T) == n:. n ~ T` `Thm* Finite(T) Prop`
int_seg	`Def {i..j} == {k:\| i k < j}` `Thm* m,n:. {m..n} Type`
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`
tm_pi	`Def (p) == Void+P(p)` `Thm* M:PM{i}. (M) Type`
tm_sigma	`Def (tm) == P(tm)+Void` `Thm* M:PM{i}. (M) Type`
tm_proto_pi	`Def P(p) == 1of(2of(2of(p)))` `Thm* p:PM{i}. P(p) Type`
tm_proto_sigma	`Def P(p) == 1of(2of(p))` `Thm* p:PM{i}. P(p) Type`
pi2	`Def 2of(t) == t.2` `Thm* B:(AType), p:a:AB(a). 2of(p) B(1of(p))`
pi1	`Def 1of(t) == t.1` `Thm* B:(AType), p:a:AB(a). 1of(p) A`
one_one_corr	`Def A ~ B == f:(AB), g:(BA). InvFuns(A; B; f; g)` `Thm* (A ~ B) Prop`
inv_funs	`Def InvFuns(A; B; f; g) == g o f = Id & f o g = Id` `Thm* f:(AB), g:(BA). InvFuns(A; B; f; g) Prop`
tidentity	`Def Id == Id` `Thm* Id AA`
compose	`Def (f o g)(x) == f(g(x))` `Thm* f:(BC), g:(AB). f o g AC`
identity	`Def Id(x) == x` `Thm* Id AA`