| Some definitions of interest. |
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adjm-graph | Def adjm-graph(A) == < vertices = A.size, edges = {p:( A.size A.size)| (A.adj(1of(p),2of(p))) }, incidence = e.e > |
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adjm-vertex-accum | Def adjm-vertex-accum(M;s',x.f(s';x);s) == primrec(M.size;s; x,s'. f(s';x)) |
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adjm_size | Def t.size == 1of(t) |
| | Thm* t:AdjMatrix. t.size  |
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adjmatrix | Def AdjMatrix == size:  size  size   |
| | Thm* AdjMatrix Type |
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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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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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list_accum | Def list_accum(x,a.f(x;a);y;l) == Case of l; nil y ; b.l' list_accum(x,a.f(x;a);f(y;b);l') (recursive) |
| | Thm* T,T':Type, l:T List, y:T', f:(T' T T'). list_accum(x,a.f(x,a);y;l) T' |
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no_repeats | Def no_repeats(T;l) == i,j: . i < ||l||  j < ||l||  i = j  l[i] = l[j] T |
| | Thm* T:Type, l:T List. no_repeats(T;l) Prop |
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primrec | Def primrec(n;b;c) == if n= 0 b else c(n-1,primrec(n-1;b;c)) fi (recursive) |
| | Thm* T:Type, n: , b:T, c:( n T T). primrec(n;b;c) T |
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upto | Def upto(i;j) == if i < j [i / upto(i+1;j)] else nil fi (recursive) |
| | Thm* i,j: . upto(i;j) {i..j } List |