`bool_arithmetic_invariant`

definition

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module: IndisputableMonolith.Foundation.DiscreteLogicRealization
domain: Foundation
line: 71 · github
papers citing: none yet

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IndisputableMonolith.Foundation.DiscreteLogicRealization on GitHub at line 71.

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formal source

  68  LogicRealization.hasIdentityStep_of_nontrivial boolRealization
  69
  70/-- Boolean realization has the same forced arithmetic as every realization. -/
  71noncomputable def bool_arithmetic_invariant (R : LogicRealization.{0, 0}) :
  72    (UniversalForcing.arithmeticOf boolRealization).peano.carrier
  73      ≃ (UniversalForcing.arithmeticOf R).peano.carrier :=
  74  ArithmeticOf.equivOfInitial
  75    (UniversalForcing.arithmeticOf boolRealization) (UniversalForcing.arithmeticOf R)
  76
  77/-- The Boolean realization's forced arithmetic has the Peano surface. -/
  78theorem bool_peano_surface :
  79    ArithmeticOf.PeanoSurface (UniversalForcing.arithmeticOf boolRealization) :=
  80  UniversalForcing.peano_surface boolRealization
  81
  82end DiscreteLogicRealization
  83end Foundation
  84end IndisputableMonolith

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