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theorem proved term proof

five_domain_product

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formal statement (Lean)

  88theorem five_domain_product :
  89    Fintype.card (SensoryModality × PrimaryEmotion × BiologicalState ×
  90                  EconomicCycle × LinguisticRole) = 3125 := by

proof body

Term-mode proof.

  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/-- $5^5 = 3125$. -/

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depends on (10)

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