metaRealizationCert_inhabited

formal source

 195  forced_arithmetic_invariance := metaForcedArithmeticInvariance
 196  arithmetic_invariance_self := metaForcedArithmeticInvariance_self
 197
 198theorem metaRealizationCert_inhabited : Nonempty MetaRealizationCert :=
 199  ⟨metaRealizationCert⟩
 200
 201/-! ## The Reflexive-Closure Theorem -/
 202
 203/-- **The framework is reflexively closed.**
 204
 205The Universal Forcing Meta-Theorem itself instantiates the Law-of-Logic
 206structural shape: the meta-cost satisfies the three definitional
 207Aristotelian conditions, and the meta-theorem itself supplies the
 208forced-arithmetic-invariance condition. The framework that proves
 209"every Law-of-Logic realization has the same forced arithmetic" is
 210itself a Law-of-Logic-shaped structure on the type of realizations.
 211
 212The forced-arithmetic-invariance condition is wrapped in `Nonempty`
 213because the equivalence is `Type 1`-valued, while the conjunction here
 214is propositional. The Nonempty wrapper is harmless: the equivalence
 215exists for every pair, so its `Nonempty` is trivially inhabited. -/
 216theorem framework_is_reflexively_closed :
 217    -- Identity, non-contradiction, totality of meta-cost are automatic:
 218    (∀ R : MetaCarrier, metaCost R R = 0) ∧
 219    (∀ R S : MetaCarrier, metaCost R S = metaCost S R) ∧
 220    (∀ R S : MetaCarrier, ∃ c : ℕ, metaCost R S = c) ∧
 221    -- The meta-theorem supplies the comparison law:
 222    (∀ R S : MetaCarrier, Nonempty (R.Orbit ≃ S.Orbit)) := by
 223  refine ⟨metaCost_self, metaCost_symm, metaCost_total, ?_⟩
 224  intro R S
 225  exact ⟨metaForcedArithmeticInvariance R S⟩
 226
 227/-! ## The Meta-Meta-Theorem -/
 228