`configDim5_equicardinal`

proved

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module: IndisputableMonolith.CrossDomain.ConfigDimUniversality
domain: CrossDomain
line: 76 · github
papers citing: none yet

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IndisputableMonolith.CrossDomain.ConfigDimUniversality on GitHub at line 76.

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formal source

  73  simp [Fintype.card_prod, hA, hB]
  74
  75/-- Two D=5 types are equicardinal (trivially, both = 5). -/
  76theorem configDim5_equicardinal
  77    {A B : Type} [Fintype A] [Fintype B]
  78    (hA : HasConfigDim5 A) (hB : HasConfigDim5 B) :
  79    Fintype.card A = Fintype.card B := by
  80  rw [hA, hB]
  81
  82/-- Concrete instance: sensory × emotion × biological = 125. -/
  83theorem three_domain_product :
  84    Fintype.card (SensoryModality × PrimaryEmotion × BiologicalState) = 125 :=
  85  triple_product_125 sensory_hasConfigDim5 emotion_hasConfigDim5 biological_hasConfigDim5
  86
  87/-- All five domains together: 5^5 = 3125. -/
  88theorem five_domain_product :
  89    Fintype.card (SensoryModality × PrimaryEmotion × BiologicalState ×
  90                  EconomicCycle × LinguisticRole) = 3125 := by
  91  have hs : Fintype.card SensoryModality = 5 := sensory_hasConfigDim5
  92  have he : Fintype.card PrimaryEmotion = 5 := emotion_hasConfigDim5
  93  have hb : Fintype.card BiologicalState = 5 := biological_hasConfigDim5
  94  have hc : Fintype.card EconomicCycle = 5 := economic_hasConfigDim5
  95  have hl : Fintype.card LinguisticRole = 5 := linguistic_hasConfigDim5
  96  simp [Fintype.card_prod, hs, he, hb, hc, hl]
  97
  98/-- $5^5 = 3125$. -/
  99theorem fivePowFive : (5 : ℕ)^5 = 3125 := by decide
 100
 101structure ConfigDimUniversalityCert where
 102  sensory_5 : HasConfigDim5 SensoryModality
 103  emotion_5 : HasConfigDim5 PrimaryEmotion
 104  biological_5 : HasConfigDim5 BiologicalState
 105  economic_5 : HasConfigDim5 EconomicCycle
 106  linguistic_5 : HasConfigDim5 LinguisticRole

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