meta_meta_theorem

formal source

 234
 235This is the reflexive-fixed-point property: `universal_forcing` is its
 236own input under the meta-realization shape. -/
 237theorem meta_meta_theorem (R S : MetaCarrier) :
 238    metaForcedArithmeticInvariance R S = universal_forcing_via_NNO R S :=
 239  rfl
 240
 241/-! ## Honest acknowledgements
 242
 243What this module *does not* prove:
 244
 245* It does not prove `universal_forcing` proves itself in the
 246  metalogical sense. Gödel-style self-reference would require a
 247  different setup involving Gödel numbering and reflection principles.
 248
 249* It does not produce a full `LogicRealization.{1, 0}` instance with
 250  every orbit/step coherence axiom. The orbit fields require design
 251  choices that are not part of the self-reference content; in
 252  particular, choosing a meaningful "step on realizations" is its own
 253  programme.
 254
 255What this module *does* prove:
 256
 257* The meta-cost on `LogicRealization.{0,0}` satisfies the three
 258  definitional Aristotelian conditions automatically.
 259
 260* The meta-theorem `universal_forcing_via_NNO` already supplies the
 261  forced-arithmetic-invariance condition that the structural shape
 262  requires.
 263
 264* The meta-realization is reflexive: comparing a realization to itself
 265  yields the identity equivalence.
 266
 267* Therefore the framework is reflexively closed in the structural