(8steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc

At: adjm-edge-accum-properties

M:AdjMatrix, T:Type, s:T, x:Vertices(adjm-graph(M)), f:(TVertices(adjm-graph(M))T). L:Vertices(adjm-graph(M)) List. (y:Vertices(adjm-graph(M)). x-adjm-graph(M)- > y (y L)) & adjm-edge-accum(M;s',x'.f(s',x');s;x) = list_accum(s',x'.f(s',x');s;L)

By:
Unfolds [`adjm-graph`;`adjm-edge-accum`] 0
THEN
Reduce 0
THEN
InstConcl [filter(M.adj(x);upto(0;M.size))]
THEN
Analyze 0


Generated subgoals:

11. M: AdjMatrix
2. T: Type
3. s: T
4. x: M.size
5. f: TM.sizeT
y:M.size. x- < vertices = M.size, edges = {p:(M.sizeM.size)| M.adj(1of(p),2of(p)) }, incidence = e.e > - > y (y filter(M.adj(x);upto(0;M.size)))
6 steps
 
21. M: AdjMatrix
2. T: Type
3. s: T
4. x: M.size
5. f: TM.sizeT
primrec(M.size;s;y,s'. if M.adj(x,y) f(s',y) else s' fi) = list_accum(s',x'.f(s',x');s;filter(M.adj(x);upto(0;M.size)))
1 step

About:
productlistifthenelseassertitnatural_numberset
lambdaapplyfunctionuniverseequalandall
exists

(8steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc