| | Some definitions of interest. |
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| adjl-graph | Def adjl-graph(G) == < vertices =  G.size, edges = x:G.size ||G.out(x)||, incidence =  e. < 1of(e),(G.out(1of(e)))[2of(e)] > > |
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| adjl_out | Def t.out == 2of(t) |
| | | Thm*  t:AdjList. t.out  t.size  (t.size List) |
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| adjl_size | Def t.size == 1of(t) |
| | | Thm* t:AdjList. t.size |
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| adjlist | Def AdjList == size:size(size List) |
| | | Thm* AdjList Type |
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| eq_adjl | Def x =A= y == x= y |
| | | Thm* A:AdjList, x,y:Vertices(adjl-graph(A)). x =A= y  |
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| eq_int | Def i=j == if i=j true ; false fi |
| | | Thm* i,j: . (i=j) |
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| gr_v | Def Vertices(t) == 1of(t) |
| | | Thm* t:Graph. Vertices(t) Type |
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| int_seg | Def {i..j } == {k:| i  k < j } |
| | | Thm* m,n:. {m..n} Type |
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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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| mkgraph | Def < vertices = v, edges = e, incidence = f > == < v,e,f,o > |
| | | Thm* v,e:Type, f:(evv), o:Top. < vertices = v, edges = e, incidence = f > Graph |
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| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
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| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) |
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| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n   n < ||l|| l[n] A |
