`strictPositiveRatio_arith_equiv_strictBoolean`

definition

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module: IndisputableMonolith.Foundation.UniversalForcing.Strict.DiscreteBoolean
domain: Foundation
line: 60 · github
papers citing: none yet

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IndisputableMonolith.Foundation.UniversalForcing.Strict.DiscreteBoolean on GitHub at line 60.

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formal source

  57
  58/-- First strict cross-realization invariance theorem:
  59positive ratios and Boolean propositions force the same arithmetic. -/
  60noncomputable def strictPositiveRatio_arith_equiv_strictBoolean
  61    (C : ComparisonOperator) (h : SatisfiesLawsOfLogic C) :
  62    (StrictLogicRealization.arith (PositiveRatio.strictPositiveRatioRealization C h)).peano.carrier
  63      ≃ (StrictLogicRealization.arith strictBooleanRealization).peano.carrier :=
  64  ArithmeticOf.equivOfInitial
  65    (StrictLogicRealization.arith (PositiveRatio.strictPositiveRatioRealization C h))
  66    (StrictLogicRealization.arith strictBooleanRealization)
  67
  68end DiscreteBoolean
  69end Strict
  70end UniversalForcing
  71end Foundation
  72end IndisputableMonolith

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