| | Who Cites adjl-graph? |
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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_size | Def t.size == 1of(t) |
| | | Thm*  t:AdjList. t.size  |
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| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(A  Type), p:(a:AB(a)). 1of(p) A |
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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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| 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: . 0 n   n < ||l|| l[n] A |
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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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| int_seg | Def {i..j } == {k:| i k < j } |
| | | Thm* m,n:. {m..n} Type |
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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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| 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 |
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| 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 |
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| lelt | Def i j < k == ij & j < k |
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| tl | Def tl(l) == Case of l; nil nil ; h.t t |
| | | Thm* A:Type, l:A List. tl(l) A List |
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| le_int | Def ij ==  j < i |
| | | Thm* i,j:. (ij)  |
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| le | Def AB == B < A |
| | | Thm* i,j:. (ij) Prop |
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| lt_int | Def i < j == if i < j true ; false fi |
| | | Thm* i,j:. (i < j) |
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| bnot | Def b == if b false else true fi |
| | | Thm* b:. b |
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| not | Def A == A False |
| | | Thm* A:Prop. (A) Prop |
