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.
Exact expanded first-order arithmetic statement
forall p n l. ((~(p = 1) /\ forall frm_prime_left_lmd_chain_prime frm_prime_right_lmd_chain_prime. p = frm_prime_left_lmd_chain_prime * frm_prime_right_lmd_chain_prime -> frm_prime_left_lmd_chain_prime = 1 \/ frm_prime_right_lmd_chain_prime = 1)) -> exists qb qc db dc. (((((exists ff_h_lmd_total_result_initial. ff_h_lmd_total_result_initial + S (n) = S ((S (0)) * qc)) /\ exists ff_q_lmd_total_result_initial. qb = ff_q_lmd_total_result_initial * S ((S (0)) * qc) + (n))) /\ forall lmd_index_total_result. (exists lmd_gap_total_result_index. lmd_gap_total_result_index + S (lmd_index_total_result) = (l)) -> exists lmd_current_total_result lmd_successor_total_result lmd_digit_total_result. ((((exists ff_h_lmd_total_result_current. ff_h_lmd_total_result_current + S (lmd_current_total_result) = S ((S (lmd_index_total_result)) * qc)) /\ exists ff_q_lmd_total_result_current. qb = ff_q_lmd_total_result_current * S ((S (lmd_index_total_result)) * qc) + (lmd_current_total_result))) /\ ((((exists ff_h_lmd_total_result_successor. ff_h_lmd_total_result_successor + S (lmd_successor_total_result) = S ((S (S lmd_index_total_result)) * qc)) /\ exists ff_q_lmd_total_result_successor. qb = ff_q_lmd_total_result_successor * S ((S (S lmd_index_total_result)) * qc) + (lmd_successor_total_result))) /\ ((((exists ff_h_lmd_total_result_digit. ff_h_lmd_total_result_digit + S (lmd_digit_total_result) = S ((S (lmd_index_total_result)) * dc)) /\ exists ff_q_lmd_total_result_digit. db = ff_q_lmd_total_result_digit * S ((S (lmd_index_total_result)) * dc) + (lmd_digit_total_result))) /\ ((lmd_current_total_result = (p) * (lmd_successor_total_result) + (lmd_digit_total_result)) /\ (exists lmd_gap_total_result_digit_bound. lmd_gap_total_result_digit_bound + S (lmd_digit_total_result) = (p))))))))Constructive proof overview
Generated structural guide
Every prime modulus admits arbitrarily long coherent constructive beta-coded base-p digit streams.
The unchanged tactic script uses 2 declared prerequisites and contains 13 exact native proof lines.
dependency-curried kernel-checked theorem body; Alpha enrollment and checked-use authority follow separately sealed release evidence; Stable membership remains unchanged
Historical empty-context replay experiment only; that experiment persisted no certificate and granted no release authority. Current checked use follows separately sealed, independently verified proof bundles; there is no Stable promotion.
Proof neighborhood
Direct dependencies
prime_nonzero Stable theorem; checked-use authorized LU0019 lucas_digit_chain_existsDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
Named ingredients (1)
01Fix variables and assumptionsL1–4
02Use earlier factsL5–8
03Fix variables and assumptionsL9–9
Work with arbitrary variables or the premises of the current implication.
- L9
intro hzero
Original exact command ledger · 13 lines
- 0001
intro p - 0002
intro n - 0003
intro l - 0004
intro hprime - 0005
specialize lucas_digit_chain_exists p - 0006
specialize lucas_digit_chain_exists n - 0007
specialize lucas_digit_chain_exists l - 0008
apply lucas_digit_chain_exists - 0009
intro hzero - 0010
specialize prime_nonzero p - 0011
apply prime_nonzero - 0012
exact hprime - 0013
exact hzero