| | Some definitions of interest. |
|
| graphobj | Def GraphObject(the_graph) == eq:Vertices(the_graph)  Vertices(the_graph)  ( x,y:Vertices(the_graph).  (eq(x,y))   x = y)(eacc:( T:Type. (TVertices(the_graph)T)TVertices(the_graph)T)(T:Type, s:T, x:Vertices(the_graph), f:(TVertices(the_graph)T).  L:Vertices(the_graph) List. (y:Vertices(the_graph). x-the_graph- > y (y  L)) & eacc(f,s,x) = list_accum(s',x'.f(s',x');s;L))(vacc:(T:Type. (TVertices(the_graph)T)TT)(T:Type, s:T, f:(TVertices(the_graph)T). L:Vertices(the_graph) List. no_repeats(Vertices(the_graph);L) & (y:Vertices(the_graph). (y L)) & vacc(f,s) = list_accum(s',x'.f(s',x');s;L))Top)) |
| | | Thm* the_graph:Graph. GraphObject(the_graph) Type{i'} |
|
| assert | Def b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| gr_v | Def Vertices(t) == 1of(t) |
| | | Thm* t:Graph. Vertices(t) Type |
|
| graph | Def Graph == v:Typee:Type(evv)Top |
| | | Thm* Graph Type{i'} |
|
| iff | Def P Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
|
| l_member | Def (x l) == i: . i < ||l|| & x = l[i] T |
| | | Thm* T:Type, x:T, l:T List. (x l) Prop |
|
| 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 |
|
| le | Def A B == B < A |
| | | Thm* i,j: . (ij) Prop |
|
| vertex-count | Def vertex-count(the_obj;x.P(x)) == ||vertex-subset(the_obj;x.P(x))|| |
|
| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l|| |
| | | Thm* ||nil|| |
|
| vertex-subset | Def vertex-subset(the_obj;x.P(x)) == the_obj.vacc(( l,x. if P(x) [x / l] else l fi),nil) |
