OAI/RingTheory/DirectFiniteness/RibbonDetachment.lean

GitHub source file

19 declarations, 0 contain sorry, 0 declared as axioms

  1. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.black_step line 17
  2. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.white_step line 21
  3. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.components_le_of_steps line 24
  4. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.black_component_invariant line 30
  5. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.white_component_invariant line 37
  6. def OAI.KaplanskyCounterexample.Planar.Ribbon.keepComponent line 44

    Source documentation

    Retain the connected component of an edge.

    def Ribbon.keepComponent (R : Ribbon α) (a : α) : Ribbon {x // R.components.r x a} :=
…

    Mentions: OAI.KaplanskyCounterexample.Planar.Ribbon

  7. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.keepComponent_card line 48
  8. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.spherical_keepComponent line 60
  9. lemma OAI.KaplanskyCounterexample.Planar.joinPair_left_iff line 70
  10. def OAI.KaplanskyCounterexample.Planar.Ribbon.detach line 83

    Source documentation

    Detach an edge from both endpoint rotations. It then forms a separate one-edge component and can be discarded by restricting to its complement.

    def Ribbon.detach (R : Ribbon α) (a : α) : Ribbon α where
…

    Mentions: OAI.KaplanskyCounterexample.Planar.Ribbon

  11. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.detach_fixed_black line 88
  12. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.detach_fixed_white line 91
  13. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.detach_isolated line 94
  14. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.detach_components_le line 114
  15. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.components_detach line 122
  16. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.detach_face line 149
  17. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.detach_face_of_face_fixed line 156
  18. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.detach_face_unplug line 162
  19. lemma OAI.KaplanskyCounterexample.Planar.Ribbon.detach_face_card_le line 169