ND0053

CRTPositiveModuliPrefix(b,c,l)

A bounded beta-coded finite prefix consisting entirely of genuinely positive moduli.

Conservative notation; not a theorem, primitive, or axiom.

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

forall gcrt_positive_index_research gcrt_positive_value_research. (exists ff_lt_gcrt_research_bound. ff_lt_gcrt_research_bound + S gcrt_positive_index_research = l) -> (((exists ff_h_gcrt_research_entry. ff_h_gcrt_research_entry + S (gcrt_positive_value_research) = S ((S (gcrt_positive_index_research)) * c)) /\ exists ff_q_gcrt_research_entry. b = ff_q_gcrt_research_entry * S ((S (gcrt_positive_index_research)) * c) + (gcrt_positive_value_research))) -> ~(gcrt_positive_value_research = 0)

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

Direct definition dependencies

Beta(b,c,i,x)Lt(a,b)

Definitions depending on this notation

none

Checked theorems using this definition

CR0001 · crt_positive_moduli_prefix_emptyCR0002 · crt_positive_moduli_prefix_drop_lastCR0003 · crt_positive_moduli_prefix_last_nonzeroCR000A · crt_positive_moduli_prefix_product_nonzeroCR0013 · crt_pairwise_coprime_prefix_solution_existsCR001B · crt_pairwise_coprime_prefix_canonical_exists_unique

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