`reality_satisfies_logic`

proved

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module: IndisputableMonolith.Foundation.LogicAsFunctionalEquation.RealityStructure
domain: Foundation
line: 75 · github
papers citing: none yet

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IndisputableMonolith.Foundation.LogicAsFunctionalEquation.RealityStructure on GitHub at line 75.

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formal source

  72  non_trivial := hT.nontrivial
  73
  74/-- Truth-evaluable comparisons satisfy the encoded laws of logic. -/
  75theorem reality_satisfies_logic
  76    (C : ComparisonOperator)
  77    (hT : TruthEvaluableComparison C) :
  78    SatisfiesLawsOfLogic C :=
  79  operative_to_laws_of_logic C
  80    (truth_eval_to_operative C hT)
  81    (truth_eval_implies_composition C hT)
  82
  83/-- Consequently, truth-evaluable finite pairwise positive-ratio comparison
  84forces the RCL family. -/
  85theorem rcl_from_truth_evaluable_comparison
  86    (C : ComparisonOperator)
  87    (hT : TruthEvaluableComparison C) :
  88    ∃ (P : ℝ → ℝ → ℝ) (c : ℝ),
  89      DAlembert.Inevitability.HasMultiplicativeConsistency (derivedCost C) P ∧
  90      (∀ u v, P u v = 2 * u + 2 * v + c * u * v) :=
  91  rcl_polynomial_closure_theorem C
  92    (truth_eval_to_operative C hT)
  93    (truth_eval_implies_composition C hT)
  94
  95end LogicAsFunctionalEquation
  96end Foundation
  97end IndisputableMonolith

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