Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.
Readable signature
BetaAt(b, c, i, x)Exact expansion
((exists ff_h_defined_beta_at. ff_h_defined_beta_at + S (x) = S ((S (i)) * c)) /\ exists ff_q_defined_beta_at. b = ff_q_defined_beta_at * S ((S (i)) * c) + (x))This node is conservative notation, not a theorem, axiom, predicate constant, or kernel rule. Its expansion remains in the unchanged first-order language.
Definition neighborhood
Depends on conservative definitions
none
Used by conservative definitions
All transitive conservative prerequisites
none
Used by theorem statements or local proof propositions
LU000C lucas_base_p_digit_prefix_point LU0015 lucas_digit_chain_initial_code_exists LU0016 lucas_digit_chain_empty LU0017 lucas_digit_chain_empty_exists LU0018 lucas_digit_chain_extend LU0019 lucas_digit_chain_exists LU001A lucas_prime_digit_chain_exists LU001B lucas_digit_chain_initial_value LU001C lucas_digit_chain_step_exists LU001D lucas_modular_backward_product_fold LU001E lucas_choose_prefix_empty LU001F lucas_choose_prefix_extend LU001G lucas_choose_prefix_exists LU001H lucas_choose_prefix_point LU001I lucas_multidigit_congruence_from_one_step LU001J lucas_terminating_multidigit_theorem_from_one_step LU001L lucas_prime_digit_chain_nonzero_index_bound LU001M lucas_prime_digit_chain_terminal_zero LU001N lucas_terminating_prime_digit_chain_exists LU001O lucas_multidigit_congruence LU001P lucas_terminating_multidigit_theorem LU001Q lucas_theorem_for_length LU001R lucas_theoremGrand-campaign planning vocabulary
Locate Beta in the global campaign vocabulary →
Reviewed BetaAt corresponds to blueprint Beta with checked argument positions [0, 1, 2, 3].
The global atlas describes planning vocabulary and does not itself certify a definition or theorem. The reviewed expansion and conservative dependency DAG on this page are the actual family-local reading definitions.