| Some definitions of interest. |
|
append | Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive) |
| | Thm* T:Type, as,bs:T List. (as @ bs) T List |
|
list-connect | Def L-G- > *x == ( y L.y-G- > *x) |
|
connect | Def x-the_graph- > *y == p:Vertices(the_graph) List. path(the_graph;p) & p[0] = x & last(p) = y |
| | Thm* For any graph
x,y:V. x-the_graph- > *y Prop |
|
gr_v | Def Vertices(t) == 1of(t) |
| | Thm* t:Graph. Vertices(t) Type |
|
graph | Def Graph == v:Type e:Type (e v v) Top |
| | Thm* Graph Type{i'} |
|
iff | Def P  Q == (P  Q) & (P  Q) |
| | Thm* A,B:Prop. (A  B) Prop |
|
l_exists | Def ( x L.P(x)) == x:T. (x L) & P(x) |
| | Thm* T:Type, L:T List, P:(T Prop). ( x L.P(x)) Prop |
|
l_member | Def (x l) == i: . i < ||l|| & x = l[i] T |
| | Thm* T:Type, x:T, l:T List. (x l) Prop |