cortical_has_6

formal source

  52  unfold HasCubeFaceCount; decide
  53theorem lepton_has_6 : HasCubeFaceCount Lepton := by
  54  unfold HasCubeFaceCount; decide
  55theorem cortical_has_6 : HasCubeFaceCount CorticalLayer := by
  56  unfold HasCubeFaceCount; decide
  57theorem braak_has_6 : HasCubeFaceCount BraakStage := by
  58  unfold HasCubeFaceCount; decide
  59theorem robotic_has_6 : HasCubeFaceCount RoboticDOF := by
  60  unfold HasCubeFaceCount; decide
  61
  62/-- The cube-face identity: 6 = 2 × 3 = face-binary × spatial-dim. -/
  63theorem cube_face_identity : (6 : ℕ) = 2 * 3 := by decide
  64
  65/-- Q₃ Euler: V - E + F = 8 - 12 + 6 = 2. -/
  66theorem q3_euler : (8 : ℤ) - 12 + 6 = 2 := by decide
  67
  68/-- Any two cube-face domains are equicardinal. -/
  69theorem cube_face_equicardinal
  70    {A B : Type} [Fintype A] [Fintype B]
  71    (hA : HasCubeFaceCount A) (hB : HasCubeFaceCount B) :
  72    Fintype.card A = Fintype.card B := by
  73  rw [hA, hB]
  74
  75/-- Standard Model total fermion count: 6 quarks + 6 leptons = 12. -/
  76theorem quark_lepton_sum :
  77    Fintype.card Quark + Fintype.card Lepton = 12 := by
  78  rw [quark_has_6, lepton_has_6]
  79
  80/-- Total with antiparticles: 2 · 12 = 24. -/
  81theorem fermion_antifermion_total :
  82    2 * (Fintype.card Quark + Fintype.card Lepton) = 24 := by
  83  rw [quark_has_6, lepton_has_6]
  84
  85/-- Three cube-face structures combine: 6³ = 216. -/