`notCollapsedToPair2`

proved

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module: IndisputableMonolith.CrossDomain.CognitiveStateSpace
domain: CrossDomain
line: 81 · github
papers citing: none yet

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IndisputableMonolith.CrossDomain.CognitiveStateSpace on GitHub at line 81.

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depends on

formal source

  78    simp only [Fintype.card_prod, senseCount, emotionCount]
  79  rw [cognitiveStateCount, h]; decide
  80
  81theorem notCollapsedToPair2 :
  82    Fintype.card CognitiveState > Fintype.card (Sense × MemorySystem) := by
  83  have h : Fintype.card (Sense × MemorySystem) = 25 := by
  84    simp only [Fintype.card_prod, senseCount, memorySystemCount]
  85  rw [cognitiveStateCount, h]; decide
  86
  87theorem notCollapsedToPair3 :
  88    Fintype.card CognitiveState > Fintype.card (Emotion × MemorySystem) := by
  89  have h : Fintype.card (Emotion × MemorySystem) = 25 := by
  90    simp only [Fintype.card_prod, emotionCount, memorySystemCount]
  91  rw [cognitiveStateCount, h]; decide
  92
  93structure CognitiveStateSpaceCert where
  94  product_count : Fintype.card CognitiveState = 125
  95  sense_surj : Function.Surjective (fun s : CognitiveState => s.1)
  96  emotion_surj : Function.Surjective (fun s : CognitiveState => s.2.1)
  97  memory_surj : Function.Surjective (fun s : CognitiveState => s.2.2)
  98  irreducible_1 : Fintype.card CognitiveState > Fintype.card Sense
  99  irreducible_2 : Fintype.card CognitiveState > Fintype.card Emotion
 100  irreducible_3 : Fintype.card CognitiveState > Fintype.card MemorySystem
 101  irreducible_pair : Fintype.card CognitiveState >
 102    Fintype.card (Sense × Emotion)
 103
 104def cognitiveStateSpaceCert : CognitiveStateSpaceCert where
 105  product_count := cognitiveStateCount
 106  sense_surj := senseProj_surj
 107  emotion_surj := emotionProj_surj
 108  memory_surj := memoryProj_surj
 109  irreducible_1 := notCollapsedToSense
 110  irreducible_2 := notCollapsedToEmotion
 111  irreducible_3 := notCollapsedToMemory

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