| | Some definitions of interest. |
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| 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))) |
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| bi-graph-edge | Def Edge(G) == {l:IdLnk| i:|G|. (l from(i)) } |
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| lconnects | Def lconnects(p;i;j)
Def == lpath(p)
Def == & (||p|| = 0  i = j Id)
Def == & ( ||p|| = 0  i = source(hd(p)) & j = destination(last(p))) |
| | | Thm* p:IdLnk List, i,j:Id. lconnects(p;i;j) Prop |
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| lpath | Def lpath(p)
Def == i: (||p||-1).
Def == destination(p[i]) = source(p[(i+1)]) & p[(i+1)] = lnk-inv(p[i]) IdLnk |
| | | Thm* p:IdLnk List. lpath(p) Prop |
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| IdLnk | Def IdLnk == Id Id  |
| | | Thm* IdLnk Type |
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| rset | Def |R| == {i:Id| (R(i)) } |
| | | Thm* R:(Id  ). |R| Type |
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| Id | Def Id == Atom  |
| | | Thm* Id Type |
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| inject | Def Inj(A; B; f) == a1,a2:A. f(a1) = f(a2) B  a1 = a2 |
| | | Thm* A,B:Type, f:(A B). Inj(A; B; f) Prop |
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| int_seg | Def {i..j } == {k: | i k < j } |
| | | Thm* m,n: . {m..n } Type |
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| l_member | Def (x l) == i: . i<||l|| & x = l[i] T |
| | | Thm* T:Type, x:T, l:T List. (x l) Prop |
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| nat | Def == {i: | 0 i } |
| | | Thm* Type |
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| le | Def A B == B<A |
| | | Thm* i,j: . (i j) Prop |
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| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l||  |
| | | Thm* ||nil||  |
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| lsrc | Def source(l) == 1of(l) |
| | | Thm* l:IdLnk. source(l) Id |
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| not | Def A == A  False |
| | | Thm* A:Prop. ( A) Prop |
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| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n: . 0 n  n<||l||  l[n] A |