WhoCites Definitions GenAutomata Sections NuprlLIB Doc

Who Cites l all?
l_allDef (xL.P(x)) == x:T. (x L) P(x)
Thm* T:Type, L:T List, P:(TProp). (xL.P(x)) Prop
l_member Def (x l) == i:. i < ||l|| & x = l[i] T
Thm* T:Type, x:T, l:T List. (x l) Prop
select Def l[i] == hd(nth_tl(i;l))
Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A
length Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive)
Thm* A:Type, l:A List. ||l||
Thm* ||nil||
nat Def == {i:| 0i }
Thm* Type
nth_tl Def nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi (recursive)
Thm* A:Type, as:A List, i:. nth_tl(i;as) A List
hd Def hd(l) == Case of l; nil "?" ; h.t h
Thm* A:Type, l:A List. ||l||1 hd(l) A
Thm* A:Type, l:A List. hd(l) A
le Def AB == B < A
Thm* i,j:. (ij) Prop
tl Def tl(l) == Case of l; nil nil ; h.t t
Thm* A:Type, l:A List. tl(l) A List
le_int Def ij == j < i
Thm* i,j:. (ij)
not Def A == A False
Thm* A:Prop. (A) Prop
lt_int Def i < j == if i < j true ; false fi
Thm* i,j:. (i < j)
bnot Def b == if b false else true fi
Thm* b:. b

Syntax:(xL.P(x)) has structure: l_all(L; T; x.P(x))

About:
listnillist_indboolbfalse
btrueifthenelseintnatural_numberaddsubtractless
less_thantokensetfunctionrecursive_def_noticeuniverse
equalmemberpropimpliesfalseallexists!abstraction

WhoCites Definitions GenAutomata Sections NuprlLIB Doc