| | Who Cites bi-graph? |
|
| bi-graph | Def bi-graph(G;to;from)
Def == i:|G|.
Def == ( l to(i).destination(l) = i
Def == & (G(source(l)))
Def == & (l from(source(l)))
Def == & (lnk-inv(l) from(i)))
Def == & ( l from(i).source(l) = i
Def == & & (G(destination(l)))
Def == & & (l to(destination(l)))
Def == & & (lnk-inv(l) to(i))) |
|
| IdLnk | Def IdLnk == Id Id  |
| | | Thm* IdLnk Type |
|
| lnk-inv | Def lnk-inv(l) == <1of(2of(l)),1of(l),2of(2of(l))> |
|
| l_all | Def ( x L.P(x)) == x:T. (x L)  P(x) |
| | | Thm* T:Type, L:T List, P:(T Prop). ( x L.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 |
|
| ldst | Def destination(l) == 1of(2of(l)) |
| | | Thm* l:IdLnk. destination(l) Id |
|
| rset | Def |R| == {i:Id| (R(i)) } |
| | | Thm* R:(Id  ). |R| Type |
|
| assert | Def b == if b True else False fi |
| | | Thm* b: . b Prop |
|
| lsrc | Def source(l) == 1of(l) |
| | | Thm* l:IdLnk. source(l) Id |
|
| Id | Def Id == Atom  |
| | | Thm* Id Type |
|
| nat | Def == {i: | 0 i } |
| | | Thm* Type |
|
| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(A Type), p:(a:A B(a)). 2of(p) B(1of(p)) |
|
| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(A Type), p:(a:A B(a)). 1of(p) A |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n: . 0 n  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||  |
|
| le | Def A B == B<A |
| | | Thm* i,j: . (i j) Prop |
|
| nth_tl | Def nth_tl(n;as) == if n 0 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 |
|
| not | Def A == A  False |
| | | Thm* A:Prop. ( A) 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 i j ==  j< i |
| | | Thm* i,j: . (i j)  |
|
| 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  |