OAI/Combinatorics/TreewidthL1/WeightedPaths.lean

GitHub source file

20 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.BoundedTreewidthL1.edgeLength line 13

    Source documentation

    Extension by zero, only used to write the sum over Walk.edges. It does not add edges or change any graph-walk length.

    noncomputable def edgeLength (e : Sym2 V) : ℝ := by
…
  2. lemma OAI.BoundedTreewidthL1.edgeLength_of_mem line 17
  3. lemma OAI.BoundedTreewidthL1.edgeLength_nonneg line 21
  4. lemma OAI.BoundedTreewidthL1.walkLength_eq_sum_edges line 28
  5. lemma OAI.BoundedTreewidthL1.walkLength_nonneg line 36
  6. lemma OAI.BoundedTreewidthL1.walkLength_pos line 42
  7. lemma OAI.BoundedTreewidthL1.walkLength_append line 49
  8. lemma OAI.BoundedTreewidthL1.walkLength_reverse line 54
  9. lemma OAI.BoundedTreewidthL1.walkLength_bypass_le line 58
  10. lemma OAI.BoundedTreewidthL1.path_length_set_finite line 66
  11. lemma OAI.BoundedTreewidthL1.path_length_set_nonempty line 77
  12. lemma OAI.BoundedTreewidthL1.shortestPathDistance_attained line 82
  13. lemma OAI.BoundedTreewidthL1.shortestPathDistance_nonneg line 86
  14. lemma OAI.BoundedTreewidthL1.shortestPathDistance_le_pathLength line 92
  15. lemma OAI.BoundedTreewidthL1.shortestPathDistance_le_walkLength line 101
  16. lemma OAI.BoundedTreewidthL1.shortestPathDistance_self line 108
  17. lemma OAI.BoundedTreewidthL1.shortestPathDistance_pos line 113
  18. lemma OAI.BoundedTreewidthL1.shortestPathDistance_comm line 119
  19. lemma OAI.BoundedTreewidthL1.shortestPathDistance_triangle line 127
  20. theorem OAI.BoundedTreewidthL1.shortestPathDistance_metric line 135