| | Some definitions of interest. |
|
| adjm_adj | Def t.adj == 2of(t) |
| | | Thm*  t:AdjMatrix. t.adj   t.size  t.size |
|
| adjm_size | Def t.size == 1of(t) |
| | | Thm* t:AdjMatrix. t.size |
|
| adjmatrix | Def AdjMatrix == size: sizesize |
| | | Thm* AdjMatrix Type |
|
| assert | Def  b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| edge | Def x-the_graph- > y ==  e:Edges(the_graph). Incidence(the_graph)(e) = < x,y > |
| | | Thm* For any graph
x,y:V. x-the_graph- > y Prop |
|
| filter | Def filter(P;l) == reduce( a,v. if P(a) [a / v] else v fi;nil;l) |
| | | Thm* T:Type, P:(T), l:T List. filter(P;l) T List |
|
| iff | Def P   Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
|
| int_seg | Def {i..j } == {k: | i  k < j } |
| | | Thm* m,n:. {m..n} Type |
|
| l_member | Def (x l) == i:. i < ||l|| & x = l[i] T |
| | | Thm* T:Type, x:T, l:T List. (x l) Prop |
|
| 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 |
|
| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
|
| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) |
|
| 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 |
