theorem
proved
term proof
observer_forcing_certificate
show as:
view Lean formalization →
formal statement (Lean)
227theorem observer_forcing_certificate :
228 -- (1) Cost is non-negative
229 (∀ e : RecognitionEvent, 0 ≤ e.cost) ∧
230 -- (2) Identity event has zero cost
231 RecognitionEvent.identity.cost = 0 ∧
232 -- (3) Identity event is persistent
233 IsPersistent RecognitionEvent.identity ∧
234 -- (4) Persistent state is unique (= 1)
235 (∀ ref : RecognitionEvent, IsPersistent ref → ref.state = 1) ∧
236 -- (5) Cooper pairing yields persistence for any positive x
237 (∀ x : ℝ, 0 < x → ∃ e : RecognitionEvent, IsPersistent e) ∧
238 -- (6) Non-trivial recognition forces an observer
239 (∀ (events : ℕ → RecognitionEvent),
240 (∃ n m : ℕ, (events n).state ≠ (events m).state) →
241 ∃ obs : Observer, obs.recognition.events = events) :=
proof body
Term-mode proof.
242 ⟨RecognitionEvent.cost_nonneg,
243 RecognitionEvent.identity_cost,
244 identity_persistent,
245 persistent_state_unique,
246 cooper_pairing_yields_persistent,
247 nontrivial_recognition_forces_observer⟩
248
249/-! ## Module Status -/
250
depends on (27)
-
has -
Observer -
RecognitionEvent -
Identity -
forces -
cost -
cooper_pairing_yields_persistent -
cost -
cost_nonneg -
identity -
identity_cost -
identity_persistent -
IsPersistent -
nontrivial_recognition_forces_observer -
Observer -
persistent_state_unique -
RecognitionEvent -
nontrivial_recognition_forces_observer -
is -
is -
for -
is -
RecognitionEvent -
is -
Cost -
Status -
identity