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def definition def or abbrev

universal_forcing_via_NNO

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formal statement (Lean)

 227noncomputable def universal_forcing_via_NNO
 228    (R S : LogicRealization.{0, 0}) : R.Orbit ≃ S.Orbit :=

proof body

Definition body.

 229  IsNaturalNumberObject.equiv (realizationOrbit_isNNO R) (realizationOrbit_isNNO S)
 230
 231/-! ## The Boolean parity-collapse theorem
 232
 233The discrete Boolean realization is the sharpest test of the iteration-object
 234versus orbit-as-set distinction. The carrier `Bool` has only two elements,
 235and the strict realization's `interpret : LogicNat → Bool` collapses
 236infinitely many iteration steps onto two values. The iteration object
 237itself never collapses; it is `LogicNat`, the natural-number object.
 238
 239The theorem below makes the collapse explicit: the Boolean interpretation
 240is exactly the parity map `Nat.bodd ∘ toNat`. -/
 241
 242namespace Strict.DiscreteBoolean
 243
 244open IndisputableMonolith.Foundation.UniversalForcing.Strict
 245
 246/-- One step of the Boolean strict realization is `xor true _`, which is
 247boolean negation. -/

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