Thm* l:AdjList. adjl_to_adjm(l) AdjMatrix | [adjl_to_adjm_wf] |
Thm* m:AdjMatrix. adjl-graph(adjm_to_adjl(m)) adjm-graph(m) | [adjm_to_adjl_graph] |
Thm* m:AdjMatrix. adjm_to_adjl(m) AdjList | [adjm_to_adjl_wf] |
Thm* M:AdjMatrix, T:Type, s:T, x:Vertices(adjm-graph(M)), f:(T Vertices(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) | [adjm-edge-accum-properties] |
Thm* M:AdjMatrix, T:Type, s:T, x:Vertices(adjm-graph(M)), f:(T Vertices(adjm-graph(M)) T). adjm-edge-accum(M;s',x'.f(s',x');s;x) T | [adjm-edge-accum_wf] |
Thm* M:AdjMatrix, T:Type, s:T, f:(T Vertices(adjm-graph(M)) T). L:Vertices(adjm-graph(M)) List. no_repeats(Vertices(adjm-graph(M));L) & ( y:Vertices(adjm-graph(M)). (y L)) & adjm-vertex-accum(M;s',x'.f(s',x');s) = list_accum(s',x'.f(s',x');s;L) | [adjm-vertex-accum-properties] |
Thm* M:AdjMatrix, T:Type, s:T, f:(T Vertices(adjm-graph(M)) T). adjm-vertex-accum(M;s',x'.f(s',x');s) T | [adjm-vertex-accum_wf] |
Thm* M:AdjMatrix, x,y:Vertices(adjm-graph(M)). x =M= y  x = y | [assert_eq_adjm] |
Thm* t:AdjMatrix. t.adj t.size  t.size   | [adjm_adj_wf] |
Thm* t:AdjMatrix. t.size  | [adjm_size_wf] |
Def adjm-rep{\\\\v:l,i:l}() == mkgraphrep(AdjMatrix, M.adjm-graph(M), M.adjm-obj{\\\\v:l,i:l}(M)) | [adjm-rep] |