ND0001 — Beta(b,c,i,x)

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.

Hygienic expanded first-order definition

((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))

The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.

Direct definition dependencies

none — first-order arithmetic only

Definitions depending on this notation

CRTPrefixLCM(b,c,l,M)CRTPrefixSolution(r,s,b,c,l,x)CRTMergeCompatiblePrefix(r,s,b,c,l)CRTPairwiseCompatiblePrefix(r,s,b,c,l)CRTPositiveModuliPrefix(b,c,l)CRTPairwiseCoprimePrefix(b,c,l)

Checked theorems using this definition

GC0006 · crt_pairwise_compatible_prefix_last GC0017 · crt_pairwise_compatible_dominating_last_solution GC0018 · crt_pairwise_compatible_dominating_last_canonical_exists_unique

Separate complete second-wave branches: Full G011 proof · Alpha v27.