`cube_face_cubed`

proved

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module: IndisputableMonolith.CrossDomain.CubeFaceUniversality
domain: CrossDomain
line: 86 · github
papers citing: none yet

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IndisputableMonolith.CrossDomain.CubeFaceUniversality on GitHub at line 86.

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depends on

formal source

  83  rw [quark_has_6, lepton_has_6]
  84
  85/-- Three cube-face structures combine: 6³ = 216. -/
  86theorem cube_face_cubed
  87    {A B C : Type} [Fintype A] [Fintype B] [Fintype C]
  88    (hA : HasCubeFaceCount A) (hB : HasCubeFaceCount B) (hC : HasCubeFaceCount C) :
  89    Fintype.card (A × B × C) = 216 := by
  90  unfold HasCubeFaceCount at hA hB hC
  91  simp [Fintype.card_prod, hA, hB, hC]
  92
  93/-- 216 = 6³. -/
  94theorem six_cubed : (6 : ℕ)^3 = 216 := by decide
  95
  96structure CubeFaceUniversalityCert where
  97  quark_6 : HasCubeFaceCount Quark
  98  lepton_6 : HasCubeFaceCount Lepton
  99  cortical_6 : HasCubeFaceCount CorticalLayer
 100  braak_6 : HasCubeFaceCount BraakStage
 101  robotic_6 : HasCubeFaceCount RoboticDOF
 102  six_equals_2_D : (6 : ℕ) = 2 * 3
 103  q3_euler : (8 : ℤ) - 12 + 6 = 2
 104  fermion_count : Fintype.card Quark + Fintype.card Lepton = 12
 105  six_cubed : (6 : ℕ)^3 = 216
 106
 107def cubeFaceUniversalityCert : CubeFaceUniversalityCert where
 108  quark_6 := quark_has_6
 109  lepton_6 := lepton_has_6
 110  cortical_6 := cortical_has_6
 111  braak_6 := braak_has_6
 112  robotic_6 := robotic_has_6
 113  six_equals_2_D := cube_face_identity
 114  q3_euler := q3_euler
 115  fermion_count := quark_lepton_sum
 116  six_cubed := six_cubed

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