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
FS000K four_square_odd_prime_half_coordinate_seed FS0014 four_square_cross_covered_prefix_bounded FS0015 four_square_cross_pigeonhole FS0016 four_square_cross_interleaved_prefix_exists FS0017 four_square_cross_intersection FS004B four_square_square_residue_prefix_exists FS004C four_square_square_residue_prefix_bounded FS004E four_square_half_square_residue_prefix_injective FS004F four_square_bounded_complement_prefix_exists FS004H four_square_complement_prefix_bounded FS004I four_square_complement_prefix_preserves_injectivity FS004K four_square_odd_prime_modular_seedGrand-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.