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% min_walk_reduced -- theorem that minimum walk is reduced
% min_walks -- minimum walk satisfying a propertyx
% path_ops -- deleting vertex and edge operations
% paths -- fundamental definition and properties about paths
% reduce_walks -- operation to reduce a walk
% sep_sets -- definition of separating sets
% di_subgraphs -- generation of di_subgraphs from vertex sets
% di_subgraphs_from_walk -- generation of di_subgraphs from walks
% subtrees -- subtrees of a digraph
% trees -- fundamental definition of trees
% walk_inductions -- induction on length of a walk
% walks -- fundamental definition and properties of walks
%
%------------------------------------------------------------------------------
top: THEORY
BEGIN
IMPORTING digraphs,
digraph_deg,
walks,
paths,
path_ops,
dags,
circuits,
cycles,
di_subgraphs,
di_subgraphs_from_walk,
digraph_ops,
max_di_subgraphs,
max_subtrees,
trees,
subtrees,
walk_inductions,
min_walk_reduced,
reduce_walks,
abstract_min,
abstract_max,
pairs,
digraph_conn_defs,
digraph_inductions,
ind_paths,
min_walks,
sep_sets,
weighted_digraphs,
wgt_digraphs_props,
Eulerian
% digraph_deg_sum -- theorem relating vertex degree and number of edges
% tree_circ -- theorem that tree has no circuits
% digraph_connected -- all connected defs are equivalent
% ramsey_new -- Ramsey's theorem
% menger -- menger's theorem
% tree_paths -- theorem that tree has only one path between vertices
% circuit_deg -- degree of circuits
% cycle_deg -- theorem about degree and existence of cycle
% digraph_complected -- unusual definition of connected digraph
% digraph_conn_piece -- structural connected ==> piece connected
% digraph_path_conn -- path connected ==> structural connected
% digraph_piece_path -- piece connected ==> path connected
% h_menger -- hard menger
% meng_scaff -- scaffolding for hard menger proof
% meng_scaff_defs -- scaffolding for hard menger proof
% meng_scaff_prelude -- scaffolding for hard menger proof
% sep_set_lems -- properties of separating sets
% digraph_deg_sum,
% tree_circ,
% digraph_connected,
% ramsey_new,
% menger,
% tree_paths, % Proof incorrect
% circuit_deg,
% cycle_deg, % not attempted yet
% digraph_complected ,
% digraph_conn_piece ,
% digraph_connected ,
% digraph_path_conn ,
% digraph_piece_path ,
% h_menger ,
% meng_scaff ,
% meng_scaff_defs ,
% meng_scaff_prelude,
% menger ,
% sep_set_lems ,
END top
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