OAI/Geometry/HyperbolicGroups/MacroCertificate.lean

GitHub source file

63 declarations, 0 contain sorry, 0 declared as axioms

  1. abbrev OAI.HyperbolicObstruction.MacroGraph.Vertex line 17

    Source documentation

    The literal 15-vertex macro graph: point and line vertices, and the single subdivision vertex of the exceptional incidence D--CD.

    abbrev Vertex := (Fin 7 ⊕ Fin 7) ⊕ Unit
  2. def OAI.HyperbolicObstruction.MacroGraph.point line 19
  3. def OAI.HyperbolicObstruction.MacroGraph.line line 20
  4. def OAI.HyperbolicObstruction.MacroGraph.exceptional line 21
  5. def OAI.HyperbolicObstruction.MacroGraph.Adjacent line 23
  6. instance OAI.HyperbolicObstruction.MacroGraph.(instance at line 31) line 31
  7. lemma OAI.HyperbolicObstruction.MacroGraph.adjacent_symm line 34
  8. lemma OAI.HyperbolicObstruction.MacroGraph.adjacent_ne line 37
  9. def OAI.HyperbolicObstruction.MacroGraph.Allowed line 43

    Source documentation

    Keep at most the specified two points, but retain every line and the subdivision vertex. Such an induced graph is a forest.

    def Allowed (p q : Fin 7) : Vertex → Prop
  | .inl (.inl i) => i = p ∨ i = q
  | _ => True

    Mentions: OAI.HyperbolicObstruction.MacroGraph.Vertex

  10. instance OAI.HyperbolicObstruction.MacroGraph.(instance at line 46) line 46
  11. def OAI.HyperbolicObstruction.MacroGraph.rank line 52

    Source documentation

    A leaf-elimination certificate, rooted at p. Ranks strictly rise towards the unique common line and the root; the exceptional rank subdivides its edge. This is a formula on the actual seven Fano vectors, not a graph hypothesis.

    def rank (p q : Fin 7) : Vertex → ℕ
  | .inl (.inl i) => if i = p then 8 else if i = q then 4 else 0
  | .inl (.inr l) => if p ≠ q ∧ Incident p l ∧ Incident q l then 6 else 2
  | .inr _ => if (3:Fin 7) = p ∨ (3:Fin 7) = q then
      if p ≠ q ∧ Incident p 4 ∧ Incident q 4 then if p = 3 then 7 else 5 else 3
    else 1

    Mentions: OAI.HyperbolicObstruction.MacroGraph.Vertex

  12. def OAI.HyperbolicObstruction.MacroGraph.Certificate line 59
  13. instance OAI.HyperbolicObstruction.MacroGraph.(instance at line 62) line 62
  14. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_0_0 line 66
  15. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_0_1 line 67
  16. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_0_2 line 68
  17. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_0_3 line 69
  18. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_0_4 line 70
  19. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_0_5 line 71
  20. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_0_6 line 72
  21. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_1_0 line 73
  22. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_1_1 line 74
  23. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_1_2 line 75
  24. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_1_3 line 76
  25. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_1_4 line 77
  26. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_1_5 line 78
  27. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_1_6 line 79
  28. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_2_0 line 80
  29. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_2_1 line 81
  30. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_2_2 line 82
  31. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_2_3 line 83
  32. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_2_4 line 84
  33. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_2_5 line 85
  34. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_2_6 line 86
  35. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_3_0 line 87
  36. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_3_1 line 88
  37. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_3_2 line 89
  38. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_3_3 line 90
  39. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_3_4 line 91
  40. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_3_5 line 92
  41. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_3_6 line 93
  42. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_4_0 line 94
  43. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_4_1 line 95
  44. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_4_2 line 96
  45. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_4_3 line 97
  46. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_4_4 line 98
  47. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_4_5 line 99
  48. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_4_6 line 100
  49. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_5_0 line 101
  50. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_5_1 line 102
  51. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_5_2 line 103
  52. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_5_3 line 104
  53. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_5_4 line 105
  54. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_5_5 line 106
  55. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_5_6 line 107
  56. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_6_0 line 108
  57. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_6_1 line 109
  58. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_6_2 line 110
  59. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_6_3 line 111
  60. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_6_4 line 112
  61. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_6_5 line 113
  62. lemma OAI.HyperbolicObstruction.MacroGraph.certificate_6_6 line 114
  63. lemma OAI.HyperbolicObstruction.MacroGraph.certificate line 116