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 qb qc db dc l i. (((((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)))))))) -> (exists lmd_gap_point_index. lmd_gap_point_index + S (i) = (l)) -> (exists q Q d. ((((exists ff_h_lmd_point_current. ff_h_lmd_point_current + S (q) = S ((S (i)) * qc)) /\ exists ff_q_lmd_point_current. qb = ff_q_lmd_point_current * S ((S (i)) * qc) + (q))) /\ ((((exists ff_h_lmd_point_next. ff_h_lmd_point_next + S (Q) = S ((S (S i)) * qc)) /\ exists ff_q_lmd_point_next. qb = ff_q_lmd_point_next * S ((S (S i)) * qc) + (Q))) /\ ((((exists ff_h_lmd_point_digit. ff_h_lmd_point_digit + S (d) = S ((S (i)) * dc)) /\ exists ff_q_lmd_point_digit. db = ff_q_lmd_point_digit * S ((S (i)) * dc) + (d))) /\ ((q = p * Q + d) /\ (exists lmd_gap_point_digit_bound. lmd_gap_point_digit_bound + S (d) = (p)))))))Constructive proof overview
Generated structural guide
Every position below an arbitrary finite chain length exposes its actual consecutive quotients and bounded base-p digit.
The unchanged tactic script uses 0 declared prerequisites and contains 14 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
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This dependency-curried candidate body does not grant checked theorem use or 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.
01Fix variables and assumptionsL1–10
02Separate the logical casesL11–11
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L11
cases hchain