theorem
proved
term proof
recognition_forcing_complete
show as:
view Lean formalization →
formal statement (Lean)
161theorem recognition_forcing_complete :
162 (∀ (S : Type) (obs : Observable S),
163 (∃ s₁ s₂, obs.value s₁ ≠ obs.value s₂) →
164 ∃ (R₁ R₂ : Type), Nonempty (Recognition.Recognize R₁ R₂)) ∧
165 (∀ (S : Type) (M : ObservableExtractionMechanism S),
166 ∃ R : RecognitionStructure S, True) ∧
167 (∀ (e : LedgerForcing.RecognitionEvent),
168 (e.ratio = 1 ↔ recognition_cost e = 0) ∧
169 (e.ratio ≠ 1 → recognition_cost e > 0)) ∧
170 (∀ (c : Configuration),
171 ∃ (e : LedgerForcing.RecognitionEvent), e.ratio = c.value) ∧
172 (∀ (S : JStableStructure),
173 ∃ (R : RecognitionLikeStructure), R.carrier = S.carrier) :=
proof body
Term-mode proof.
174 ⟨recognition_necessary,
175 fun _ M => ⟨recognition_from_extraction M, trivial⟩,
176 recognition_is_cost_structure,
177 cost_minima_are_recognition,
178 stability_forces_recognition⟩
179
180/-! ## Part 5: Ledger Forcing -/
181
depends on (30)
-
RecognitionStructure -
carrier -
carrier -
Configuration -
RecognitionEvent -
RecognitionEvent -
Configuration -
cost_minima_are_recognition -
JStableStructure -
Observable -
ObservableExtractionMechanism -
recognition_cost -
recognition_from_extraction -
recognition_is_cost_structure -
RecognitionLikeStructure -
recognition_necessary -
RecognitionStructure -
stability_forces_recognition -
RecognitionEvent -
Observable -
value -
Observable -
M -
RecognitionStructure -
Recognize -
M -
S -
RecognitionStructure -
Recognize -
RecognitionStructure